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Page No 142:
Question 1:
Convert each of the following fraction into a percentage:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
Answer:
We have the following:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
Page No 142:
Question 2:
Convert each of the following into a fraction:
(i) 32%
(ii)
(iii)
(iv) 120%
(v) 6.25%
(vi) 0.8%
(vii) 0.06%
(viii) 22.75%
Answer:
We have the following:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
Page No 142:
Question 3:
Express each of the following as a ratio:
(i) 43%
(ii) 36%
(iii) 7.5%
(iv) 125%
Answer:
We have:
(i)
(ii)
(iii)
(iv)
Page No 142:
Question 4:
Convert each of the following ratios into a percentage:
(i) 37 : 100
(ii) 16 : 25
(iii) 3 : 5
(iv) 5 : 4
Answer:
We have the following:
(i) 37 : 100 =
(ii) 16 : 25 =
(iii) 3 : 5 =
(iv) 5 : 4 =
Page No 142:
Question 5:
Convert each of the following into decimal form:
(i) 45%
(ii) 127%
(iii) 3.6%
(iv) 0.23%
Answer:
We have the following:
(i) 45% =
(ii) 127% =
(iii) 3.6% =
(iv) 0.23% =
Page No 142:
Question 6:
Convert each of the following decimals into a percentage:
(i) 0.6
(ii) 0.42
(iii) 0.07
(iv) 0.005
Answer:
We have:
(i) 0.6 = (0.6 100)% = 60%
(ii) 0.42 = (0.42 100)% = 42%
(iii) 0.07 = (0.07 100)% = 7%
(iv) 0.005 = (0.005 100)% = 0.5%
Page No 142:
Question 7:
Find:
(i) 32% of 425
(ii)
(iii) 6.5% of 400
(iv) 136% of 70
(v) 2.8% of 35
(vi) 0.6% of 45
Answer:
We have:
(i) 32% of 425 =
(ii) of 16 = of 16 =
(iii) 6.5% of 400 =
(iv) 136% of 70 =
(v) 2.8% of 35 =
(vi) 0.6% of 45 =
Page No 142:
Question 8:
Find:
(i) 25% of Rs 76
(ii) 20% of Rs 132
(iii) 7.5% of 600 m
(iv)
(v) 8.5% of 5 kg
(vi) 20% of 12 litres
Answer:
We have the following:
(i) 25% of Rs 76 = Rs = Rs = Rs 19
(ii) 20% of Rs 132 = Rs = Rs = Rs 26.4
(iii) 7.5% of 600 m =
(iv) of 90 km = of 90 km =
(v) 8.5% of 5 kg = [∵1 kg = 1000 g]
(vi) 20% of 12 L =
Page No 142:
Question 9:
Find the number whose 13% is 65.
Answer:
Let x be the required number.
Then, 13% of x = 65
⇒
⇒ x =
Hence, the required number is 500.
Page No 142:
Question 10:
Find the number whose is 2.
Answer:
Let x be the required number.
Then, of x = 2
⇒
⇒
⇒ x =
Hence, the required number is 32.
Page No 143:
Question 11:
What amount is 10% more than Rs 90?
Answer:
10% of Rs 90 = Rs = Rs 9
∴ Amount that is 10% more than Rs 90 = Rs (90 + 9) = Rs 99
Hence, the required amount is Rs 99.
Page No 143:
Question 12:
What amount is 20% less than Rs 60?
Answer:
20% of Rs 60 = Rs = Rs 12
∴ Amount that is 20% less than Rs 60 = Rs (60 − 12) = Rs 48
Hence, the required amount is Rs 48.
Page No 143:
Question 13:
If 3% of x is 9, find the value of x.
Answer:
3% of x = 9
⇒
⇒ x =
Hence, the value of x is 300.
Page No 143:
Question 14:
If 12.5% of x is 6, find the value of x.
Answer:
12.5% of x = 6
⇒
⇒ x =
Hence, the value of x is 48.
Page No 143:
Question 15:
What per cent of 84 is 14?
Answer:
Let x% of 84 be 14.
Then,
⇒
⇒ x =
Hence, of 84 is 14.
Page No 143:
Question 16:
What percentage is
(i) Rs 15 of Rs 120?
(ii) 36 minutes of 2 hours?
(iii) 8 hours of 2 days
(iv) 160 metres of 4 km?
(v) 175 mL of 1 litre?
(vi) 25 paise of Rs 4?
Answer:
(i) Let x% of Rs 120 be Rs 15.
Then, Rs = Rs 15
⇒ = 15
∴ x = = = 12.5%
Hence, 12.5% of Rs 120 is Rs 15.
(ii) Let x% of 2 h be 36 min.
Then, min = 36 min
⇒ = 36
∴ x = = 30%
Hence, 30% of 2 h is 36 min.
(iii) Let x% of 2 days be 8 h.
Then, h = 8 h
⇒ = 8
∴ x = =
Hence, of 2 days is 8 h.
(iv) Let x% of 4 km be 160 m.
Then, m = 160 m
⇒ 40x = 160
∴ x = = 4%
Hence, 4% of 4 km is 160 m.
(v) Let x% of 1 L be 175 mL.
Then, mL = 175 mL
⇒ 10x = 175
∴ x = = 17.5%
Hence, 17.5% of 1 L is 175 mL.
(vi) Let x% of Rs 4 be 25 paise.
Then, paise = 25 paise
⇒ 4x = 25
∴ x = =
Hence, of Rs 4 is 25 paise.
Page No 147:
Question 1:
Rupesh secures 495 marks out of 750 in his annual examination. Find the percentage of marks obtained by him.
Answer:
Maximum marks of the examination = 750
Marks secured by Rupesh = 495
Percentage of marks secured = = 66%
Hence, Rupesh scored 66% in the examination.
Page No 147:
Question 2:
The monthly salary of a typist is Rs 15625. If he gets an increase of 12%, find his new salary.
Answer:
Total monthly salary = Rs 15625
Increase percentage = 12%
∴ Amount increase = 12% of Rs 15625
= Rs = Rs 1875
∴ New salary = Rs 15625 + Rs 1875
= Rs 17500
Hence, the new salary of the typist is Rs 17,500.
Page No 147:
Question 3:
The excise duty on a certain item has been reduced to Rs 760 from Rs 950. Find the reduction per cent in the excise duy on that item.
Answer:
Original excise duty on the item = Rs 950
Amount reduced on excise duty = Rs (950 − 760) = Rs 190
∴ Reduction percent =
= = 20
Hence, the excise duty on that item is reduced by 20%.
Page No 147:
Question 4:
96% of the cost of a TV is Rs 10464. What is its total cost?
Answer:
Let Rs x be the total cost of the TV set.
Now, 96% of the total cost of TV = Rs 10464
⇒ 96% of Rs x = Rs 10464
⇒ = 10464
∴ x = = 10900
Hence, the total cost of the TV set is Rs 10900.
Page No 147:
Question 5:
70% of the students in a school are boys and the number of girls is 504. Find the number of boys in the school.
Answer:
Let the total number of students be 100.
Then, number of boys = 70
∴ Number of girls = (100 − 70) = 30
Now, total number of students when the number of girls is 30 = 100
Then, total number of students when the number of girls is 504 = = 1680
∴ Number of boys = (1680 − 504) = 1176
Hence, there are 1176 boys in the school.
Page No 147:
Question 6:
An ore contains 12% copper. How many kilograms of the ore are required to get 69 kg of copper?
Answer:
Let x kg be the amount of the required ore.
Then, 12% of x kg = 69 kg
⇒ kg = 69 kg
⇒ x = kg = 575 kg
Hence, 575 kg of ore is required to get 69 kg of copper.
Page No 147:
Question 7:
36% of the maximum marks are required to pass a test. A student gets 123 marks and is declared failed by 39 marks. Find the maximum marks.
Answer:
Let x be the maximum marks.
Pass marks = (123 + 39) = 162
Then, 36% of x = 162
⇒
⇒ x = = 450
∴ Maximum marks = 450
Page No 147:
Question 8:
A fruit-seller had some apples. He sells 40% of them and still has 420 apples. Find the number of apples he had originally.
Answer:
Suppose that the fruit seller initially had 100 apples.
Apples sold = 40
∴ Remaining apples = (100 − 40) = 60
Initial amount of apples if 60 of them are remaining = 100
Initial amount of apples if 1 of them is remaining =
Initial amount of apples if 420 of them are remaining = = 700
Hence, the fruit seller originally had 700 apples.
Page No 147:
Question 9:
In an examination, 72% of the total examinees passed. If the number of failures is 392, find the total number of examinees.
Answer:
Suppose that 100 candidates took the examination.
Number of passed candidates = 72
Number of failed candidates = (100 − 72) = 28
Total number of candidates if 28 of them failed = 100
Total number of candidates if 392 of them failed = = 1400
Hence, the total number of examinees is 1400.
Page No 147:
Question 10:
After decuting a commission of 5%, a moped costs Rs 15200. What is its gross value?
Answer:
Suppose that the gross value of the moped is Rs x.
Commission on the moped = 5%
Price of moped after deducting the commission = Rs ( x − 5% of x)
= Rs = Rs = Rs
Now, price of the moped after deducting the commission = Rs 15200
Then, Rs = Rs 15200
∴ x = Rs = Rs (160 100) = Rs 16000
Hence, the gross value of the moped is Rs 16000.
Page No 147:
Question 11:
Gunpowder contains 75% of nitre and 10% of sulphur, and the rest of it is charcoal. Find the amount of charcoal in 8 kg of gunpowder.
Answer:
Total quantity of gunpowder = 8 kg = 8000 g (1 kg = 1000 g)
Quantity of nitre in it = 75% of 8000 g
= g = 6000 g = 6 kg
Quantity of sulphur in it = 10% of 8000 g
= g = 800 g = 0.8 kg
∴ Quantity of charcoal in it = {8000 − (6000 + 800)} g
= (8000 − 6800) g
= 1200 g = 1.2 kg
Hence, the amount of charcoal in 8 kg of gunpowder is 1.2 kg.
Page No 147:
Question 12:
Chalk contains 3% of carbon, 10% of calcium and 12% of oxygen. Find the amount in grams of each of these substances in 1 kg of chalk.
Answer:
Total quantity of chalk = 1 kg = 1000 g
Now, we have the following:
Quantity of carbon in it = 3% of 1000 g
= = 30 g
Quantity of calcium in it = 10% of 1000 g
= g = 100 g
Quantity of oxygen in it = 12% of 1000 g
= g = 120 g
Page No 148:
Question 13:
Sonal went to school for 219 days in a full year. If her attendance is 75%, find the number of days on which the school was open.
Answer:
Let x be the total number of days on which the school was open.
Number of days when Sonal went to school = 219
Percentage of attendance = 75
Thus, 75% of x = 219
⇒
∴ x = days
Hence, the school was open for a total of 292 days.
Page No 148:
Question 14:
3% commission on the sale of a property amounts to Rs 42660. What is the total value of the property?
Answer:
Let the total value of the property be Rs x.
Percentage of commission = 3
Amount of commission = Rs 42660
Thus, 3% of Rs x = Rs 42660
⇒ = 42660
∴ x =
Hence, the total value of the property is Rs 14,22,000.
Page No 148:
Question 15:
In an election, there were two candidates A and B. The total number of voters in this constituency was 60000 and 80% of the total votes were polied. If 60% of the polied votes were cast in favour of A, how many votes were received by B?
Answer:
Total number of eligible voters = 60000
Number of voters who gave their votes = 80% of 60000
= = 48000
Number of votes in favour of candidate A = 60% of 48000
= = 28800
∴ Number of votes received by candidate B = (48000 − 28800) = 19200
Hence, candidate B recieved 19,200 votes.
Page No 148:
Question 16:
The price of a shirt is reduced by 12% in a discount sale. If its present price is Rs 1188, find its original price.
Answer:
Let us assume that the original price of the shirt is Rs x.
Discount on the shirt = 12%
So, value of discount on the shirt = 12% of Rs x
= Rs = Rs
Value of the shirt after discount = Rs
= Rs = Rs
Present price of the shirt = Rs 1188
Then, Rs = Rs 1188
⇒ 88x = (1188 100)
⇒ 88x = 118800
∴ x = = 1350
Hence, the original price of the shirt is Rs 1350.
Page No 148:
Question 17:
The price of a sweater is increased by 8%. If its increased price is Rs 1566, find the original price.
Answer:
Let us assume that the original price of the sweater is Rs. x
Increased percentage = 8%
So, value of increase on the sweater = 8% of Rs x
= Rs = Rs
Increased price of the sweater = Rs
= Rs = Rs
However, increased price of the sweater = Rs 1566
Then, Rs = Rs 1566
∴ x = = 1450
Hence, the original price of the sweater is Rs 1450
Page No 148:
Question 18:
After spending 80% of his income and giving 10% of the remainder in a charity, a man has Rs 46260 left with him. Find his income.
Answer:
Let the income of the man be Rs x.
Then, income spent = 80% of Rs. x
= Rs = Rs = Rs
Amount left after all the expenditure = Rs = Rs = Rs
Amount given to the charity = 10% of Rs
= Rs = Rs = Rs
Amount left after the charity = Rs
= Rs = Rs
Now, we have:
Rs = Rs 46260
∴ x = Rs = Rs 257000
Hence, the income of the man is Rs 2,57,000.
Page No 148:
Question 19:
A number is increased by 20% and the increased number is decreased by 20%. Find the net increase of decrease per cent.
Answer:
Let the number be 100.
Increase in the number = 20%
Increased number = (100 + 20) =120
Now, decrease in the number = (20% of 120)
=
New number = (120 − 24) = 96
Net decrease = (100 − 96) = 4
Net decrease percentage = = 4
Hence, the net decrease is 4%.
Page No 148:
Question 20:
The salary of an officer is increased by 20%. By what percentage should the new salary be reduced to restore the original salary?
Answer:
Let the original salary be Rs 100.
Increase in it = 20%
Salary after increment = Rs (100 + 20) = Rs 120
To restore the original salary, reduction required = Rs (120 − 100) = Rs 20
Reduction on Rs 120 = Rs 20
∴ Reduction percentage = = =
Hence, the required reduction on the new salary is .
Page No 148:
Question 21:
A property dealer charges commission at the rate of 2% on the first Rs 200000, 1% on the next Rs 200000 and 0.5% on the remaining price. Find his commission on the property that has been sold for Rs 540000.
Answer:
Total cost of the property = Rs 540000
Commission on the first Rs 200000 = 2% of Rs 200000
= = Rs 4000
Commission on the next Rs 200000 = 1% of Rs 200000
= = Rs 2000
Remaining amount = Rs (540000 − 400000) = Rs 140000
∴ Commission on Rs 140000 = 0.5% of Rs 140000
= Rs
= Rs = Rs 700
Thus, total commission on the property worth Rs 540000 = Rs (4000 + 2000 + 700)
= Rs 6700
Hence, the commission of the property dealer on the property that has been sold for Rs 540000 is Rs 6700.
Page No 148:
Question 22:
Nikhil's income is 20% less than that of Akhil. How much per cent is Akhil's income more than that of Nikhil's?
Answer:
Let Akhil's income be Rs 100.
∴ Nikhil's income = Rs 80
Akhil's income when Nikhil's income is Rs 80 = Rs 100
Akhil's income when Nikhil's income is Rs 100 = Rs = Rs 125
i.e., if Nikhil's income is Rs.100, then Akhil's income is Rs 125.
Hence, Akhil's income is more than that of Nikhil's by 25%.
Page No 148:
Question 23:
Jhon's income is 20% more than that of Mr Thomas. How much per cent is the income of Mr Thomas less than that of John?
Answer:
Let Rs 100 be the income of Mr. Thomas.
∴ John's income = Rs 120
Mr. Thomas' income when John's income is Rs 120 = Rs 100
Mr. Thomas' income when John's income is Rs 100 = Rs = Rs
Hence, Mr Thomas' income is less than that of John's by .
Page No 148:
Question 24:
The value of a machine depreciated 10% every year. If its present value is Rs 387000, what was its value 1 year ago?
Answer:
Let Rs x be the value of the machine one year ago.
Then, its present value = 90% of Rs x
= Rs = Rs
It is given that present value of the machine = Rs 387000
⇒ x = Rs = Rs = Rs 430000
Hence, the value of the machine a year ago was Rs 430000.
Page No 148:
Question 25:
The value of a car decreases annually by 20%. If the present value of the car be Rs 450000, what will be its value after 2 years?
Answer:
The present value of the car = Rs 450000
The decrease in its value after the first year = 20% of Rs 450000
= Rs = Rs 90000
The depreciated value of the car after the first year = Rs (450000 − 90000) = Rs 360000
The decrease in its value after the second year = 20% of Rs 360000
= Rs = Rs 72000
The depreciated value of the car after the second year = Rs (360000 − 72000) = Rs 288000
Hence, the value of the car after two years will be Rs 288000.
Page No 148:
Question 26:
The population of a town increases 10% annually. If its present population is 60000, what will be its population after 2 years?
Answer:
Present population of the town = 60000
Increase in population of the town after the 1 year = 10% of 60000
= = 6000
Thus, population of the town after 1 year = 60000 + 6000 = 66000
Increase in population after 2 years = 10% of 66000
= = 6600
Thus, population after the second year = 66000 + 6600 = 72600
Hence, the population of the town after 2 years will be 72600.
Page No 148:
Question 27:
Due to an increase in the price of sugar by 25%, by how much per cent must a householder decrease the consumption of sugar so that there is no increase in the expenditure on sugar?
Answer:
Let the consumption of sugar originally be 1 unit and let its cost be Rs 100
New cost of 1 unit of sugar = Rs 125
Now, Rs 125 yield 1 unit of sugar.
∴ Rs 100 will yield unit = unit of sugar.
Reduction in consumption = = unit
∴ Reduction percent in consumption = %= %= 20%
Page No 148:
Question 1:
Mark (✓) against the correct answer
as rate per cent is
(a) 7.5%
(b) 75%
(c) 0.75%
(d) none of these
Answer:
(b) 75%
= = 75%
Page No 148:
Question 2:
Mark (✓) against the correct answer
The ratio 2 : 5 as rate per cent is
(a) 4%
(b) 0.4%
(c) 40%
(d) 14%
Answer:
(c) 40%
2 : 5 = = = 40%
Page No 148:
Question 3:
Mark (✓) against the correct answer
expressed as a fraction, is
(a)
(b)
(c)
(d)
Answer:
(c)
= =
Page No 149:
Question 4:
Mark (✓) against the correct answer
If x% of 75 = 9, then the value of x is
(a) 16
(b) 14
(c) 12
(d) 8
Answer:
(c) 12
We have x% of 75 = 9
⇒
∴ x =
Hence, the value of x is 12
Page No 149:
Question 5:
Mark (✓) against the correct answer
What per cent of is ?
(a) 25%
(b) 20%
(c) 15%
(d) 10%
Answer:
(d) 10%
Let x be the required percent.
Then, x % of =
⇒
∴ x = = 10
Hence, 10% of is
Page No 149:
Question 6:
Mark (✓) against the correct answer
What per cent of 1 day is 36 minutes?
(a) 25%
(b) 2.5%
(c) 3.6%
(d) 0.25%
Answer:
(b) 2.5%
Let x % of 1 day be 36 min.
Then, min = 36 min
∴ x = =
Hence, 2.5% of 1 day is 36 min.
Page No 149:
Question 7:
Mark (✓) against the correct answer
A number increased by 20% gives 42. The number is
(a) 35
(b) 28
(c) 36
(d) 30
Answer:
(a) 35
Let the required number be x.
Then, x + 20% of x = 42
⇒
⇒
⇒ [∵ LCM of 1 and 5 = 5]
⇒
∴ x =
Hence, the required number is 35.
Page No 149:
Question 8:
Mark (✓) against the correct answer
A number decreased by 8% gives 69. The number is
(a) 80
(b) 75
(c) 85
(d) none of these
Answer:
(b) 75
Let the required number be x.
Then, x − 8% of x = 69
⇒ = 69
⇒ = 69
⇒ = 69 [Since L.C.M. of 1 and 25 = 25]
⇒
∴ x = = 75
Hence, the required number is 75
Page No 149:
Question 9:
Mark (✓) against the correct answer
An ore contains 5% copper. How much ore is required to obtain 400 g of copper?
(a) 2 kg
(b) 4 kg
(c) 6 kg
(d) 8 kg
Answer:
(d) 8 kg
Let x kg be the required amount of ore.
Then, 5% of x kg = 400 g = 0.4 kg [∵ 1 kg = 1000 g]
⇒
⇒ x = = 8
Hence, 8 kg of ore is required to obtain 400 g of copper.
Page No 149:
Question 10:
Mark (✓) against the correct answer
After deducting a commission of 10% a TV costs Rs 18000. What is its gross value?
(a) Rs 18800
(b) Rs 20000
(c) Rs 19800
(d) none of these
Answer:
(b) Rs. 20000
Suppose that the gross value of the TV is Rs x.
Commission on the TV = 10%
Price of the TV after deducting the commission = Rs (x − 10% of x)
= Rs = Rs = Rs
However, price of the TV after deducting the commission = Rs 18000
Then, Rs = Rs 18000
∴ x = = Rs (2000 10) = Rs 20000
Hence, the gross value of the TV is Rs 20,000
Page No 149:
Question 11:
Mark (✓) against the correct answer
On increasing the salary of a man by 25%, it becomes Rs 20000. What was his original salary?
(a) Rs 15000
(b) Rs 16000
(c) Rs 18000
(d) Rs 25000
Answer:
(b) Rs. 16000
Let us assume that the original salary of the man is Rs x.
Increase in it = 25%
Value increased in the salary = 25% of Rs. x
= Rs = Rs
Salary after increment= Rs = Rs
However, increased salary = Rs 20000
Then, Rs = Rs 20000
∴ x = Rs = Rs 16000
Hence, the original salary of the man is Rs 16,000
Page No 149:
Question 12:
Mark (✓) against the correct answer
In an examination, 95% of the total examinees passed. If the number of failures is 28, how many examinees were there?
(a) 600
(b) 480
(c) 560
(d) 840
Answer:
(c) 560
Suppose that the number of examinees is 100.
Number of passed examinees = 95
Number of failed examinees = (100 − 95) = 5
Total number of examinees if 5 of them failed = 100
Total number of examinees if 28 of them failed =
Hence, there were 560 examinees.
Page No 149:
Question 13:
Mark (✓) against the correct answer
A fruit-seller had some apples. He sells 40% of them and still has 420 apples. How many apples had he in all?
(a) 588
(b) 600
(c) 700
(d) 725
Answer:
(c) 700
Suppose that the fruit seller initially had 100 apples.
Number of apples sold = 40
∴ Number of remaining apples = (100 − 40) = 60
Initial number of apples if 60 of them are remaining = 100
Initial number of apples if 420 of them are remaining = = 700
Hence, the fruit seller originally had 700 apples with him.
Page No 149:
Question 14:
Mark (✓) against the correct answer
The value of a machine depreciated 10% annually. If its present value is Rs 25000, what will be its value after 1 year?
(a) Rs 27500
(b) Rs 22500
(c) Rs 25250
(d) none of these
Answer:
(c) Rs. 25250
Present value of the machine = Rs 25000
Decrease in its value after 1 year = 10% of Rs 25000
= Rs = Rs 2500
Depreciated value after 1 year = Rs (25000 − 2500) = Rs 22500
Hence, the value of the machine after 1 year will be Rs 22500
Page No 149:
Question 15:
Mark (✓) against the correct answer
8% of a number is 6. What is the number?
(a) 48
(b) 96
(c) 75
(d) 60
Answer:
(c) 75
Let the required number be x. Then, we have:
8% of x = 6
⇒
∴ x =
Hence, the required number is 75
Page No 149:
Question 16:
Mark (✓) against the correct answer
60% of 450 = ?
(a) 180
(b) 210
(c) 270
(d) none of these
Answer:
(c) 270
60% of 450 =
= = (3 90) = 270
Page No 149:
Question 17:
Mark (✓) against the correct answer
On reducing the value of a chair by 6% it becomes Rs 658. The original value of the chair is
(a) Rs 750
(b) Rs 720
(c) Rs 500
(d) Rs 700
Answer:
(d) Rs. 700
Let us assume that the original price of the chair is Rs x.
Reduce percentage on the chair = 6%
So, value of reduction on the chair = 6% of Rs. x
= Rs = Rs
Reduced price of the chair = Rs
= Rs = Rs
However, present price of the chair = Rs 658
Then, Rs = Rs 658
⇒ Rs = Rs 658
⇒ x = Rs = Rs
Hence, the original price of the chair is Rs 700
Page No 149:
Question 18:
Mark (✓) against the correct answer
70% of students in a school are boys. If the number of girls is 240, how many boys are there in the school?
(a) 420
(b) 560
(c) 630
(d) 480
Answer:
(b) 560
Let the total number of students be 100.
Then, number of boys = 70
∴ Number of girls = (100 − 70) = 30
Now, total number of students if there are 30 girls = 100
Total number of students if there are 240 girls =
∴ Number of boys = (800 − 240) = 560
Hence, there are 560 boys in the school.
Page No 149:
Question 19:
Mark (✓) against the correct answer
If 11% of a number exceeds 7% of the number by 18, the number is
(a) 72
(b) 360
(c) 450
(d) 720
Answer:
(c) 450
Let x be the number.
(11% of x) − (7% of x) = 18
⇒
⇒
∴ x =
Hence, the required number is 450
Page No 149:
Question 20:
Mark (✓) against the correct answer
If 35% of a number added to 39 is the number itself, the number is
(a) 60
(b) 65
(c) 75
(d) 105
Answer:
(a) 60
Let x be the number.
According to question, we have:
(35% of x ) + 39 = x
⇒
⇒
⇒
⇒
⇒
∴ x = = 60
Hence, the required number is 60
Page No 149:
Question 21:
Mark (✓) against the correct answer
In an examination it is required to get 36% to pass. A student gets 145 marks and fails by 35 marks. The maximum marks are
(a) 400
(b) 450
(c) 500
(d) 600
Answer:
(c) 500
Let x be the maximum marks.
Pass marks = (145 + 35) = 180
∴ 36% of x = 180
⇒
⇒ x =
Hence, maximum marks = 500
Page No 150:
Question 22:
Mark (✓) against the correct answer
A number decreased by 40% gives 135. The number is
(a) 175
(b) 200
(c) 250
(d) 225
Answer:
(d) 225
Let x be the number.
According to question, we have:
x − 40% of x = 135
⇒
⇒
⇒
⇒ x = = 225
Hence, the required number is 225
Page No 151:
Question 1:
Convert:
(i) into a percentage
(ii) into a percentage
(iii) 45% into a percentage
(iv) 105% into a percentage
(v) 15% into a percentage
(vi) 12 : 25 into a percentage
Answer:
We have:
(i) =
(ii) =
(iii) 45% =
(iv) 105% =
(v) 15% == 3 : 20
(vi) 12 : 25 =
Page No 151:
Question 2:
(i) What per cent of 1 kg is 125 g?
(ii) What per cent of 80 m is 24 m?
Answer:
(i) Let x% of 1 kg be 125g.
Then,
⇒ 10x = 125
⇒ x =
Hence, of 1 kg is 125 g.
(ii) Let x% of 80 m be 24 m.
Then,
⇒ = 24
⇒ x =
Hence, of 80 m is 24 m.
Page No 151:
Question 3:
(i) Find of 30.
(ii) Find 15% of Rs 140
Answer:
(i) of 30 = of 30
=
= 5
(ii) 15% of Rs 140 = Rs
= Rs (3 7)
= Rs 21
Page No 151:
Question 4:
(i) Find the number whose is 5.
(ii) Find 0.8% of 45.
Answer:
(i) Let x be the required number.
Then, of x = 5
⇒ of x = 5
⇒
⇒
∴ x = (5 16) = 80
Hence, the required number is 80.
(i) 0.8% of 45 =
=
=
Hence, 0.8% of 45 is 0.36.
Page No 151:
Question 5:
A number is increased by 10% and the increased number is decreased by 10%. Show that the net decrease is 1%.
Answer:
Let x be the number.
The number is increased by 10%.
∴ Increased number = 110% of x =
The number is, then, decreased by 10%.
∴ Decreased number = 90% of =
Net decrease =
Net decrease percentage =
Page No 151:
Question 6:
The value of a machine depriciates at the rate of 10% per annum. If its present value is Rs 10000, what will be its value after 2 years?
Answer:
The present value of the machine = Rs 10000
The decrease in its value after the 1st year = 10% of Rs 10000
= Rs = Rs 1000
The depreciated value of the machine after the 1st year = Rs (10000 − 1000) =Rs 9000
The decrease in its value after the 2nd year = 10% of Rs 9000
= Rs = Rs 900
The depreciated value of the machine after the 2nd year = Rs (9000 − 900) = Rs 8100
Hence, the value of the machine after two years will be Rs 8100.
Page No 151:
Question 7:
The population of a town increases at 5% per annum. Its present population is 16000. What will be its population after 2 years?
Answer:
The present population of the town = 16000
Increase in population after 1 year = 5% of 16000
= = 800
Thus, population after one year = 16000 + 800 = 16800
Increase in population after 2 years = 5% of 16800
= = 840
Increased population after two years = 16800 + 840 = 17640
Hence, the population of the town after two years will be 17,640.
Page No 151:
Question 8:
The price of a teaset is increased by 5%. If the increased price is Rs 441, what is its original price?
Answer:
Let us assume that the original price of the tea set is Rs. x
Increase in it = 5%
So, value increased on the tea set = 5% of Rs. x
= Rs. = Rs.
Then, increased price of the tea set = Rs.
= Rs. = Rs.
However, increased price = Rs. 441
Then, Rs. = Rs. 441
∴ x = = 420
Hence, the original price of the tea set is Rs 420
Page No 151:
Question 9:
Mark (✓) against the correct answer
expressed as a fraction is
(a)
(b)
(c)
(d)
Answer:
(b)
= =
Page No 151:
Question 10:
Mark (✓) against the correct answer
If x% of 75 = 12, then the value of x is
(a) 8
(b) 10
(c) 12
(d) 16
Answer:
(c) 12
Given that x% of 75 = 12
Then,
⇒ x = =16
Hence, the value of x is 16
Page No 151:
Question 11:
Mark (✓) against the correct answer
A number increased by 20% gives 30. The number is
(a) 150
(b) 6
(c) 25
(d) 60
Answer:
(c) 25
Let the number be x. Then, we have:
120% of x = increased number
⇒ 30 =
⇒ 30 =
⇒ x =
Hence, the required number is 25
Page No 151:
Question 12:
Mark (✓) against the correct answer
5% of a number is 9. The number is
(a) 120
(b) 140
(c) 160
(d) 180
Answer:
(d) 180
Let the required number be x. Then, we have:
5% of x = 9
⇒
⇒ x =
Page No 151:
Question 13:
Mark (✓) against the correct answer
If 35% of a number added to 39 is the number itself, the number is
(a) 60
(b) 65
(c) 75
(d) 70
Answer:
(a) 60
Let the number be x.
According to question, we have:
(35% of x ) + 39 = x
⇒
⇒
⇒
⇒
⇒
∴ x = = 60
Hence, the required number is 60.
Page No 151:
Question 14:
Mark (✓) against the correct answer
In an examination it is required to get 36% to pass. A student gets 160 marks and fails by 20 marks. The maximum marks are
(a) 400
(b) 450
(c) 500
(d) 600
Answer:
(c) 500
Let x be the maximum marks.
Pass marks = (160 + 20) = 180
∴ 36% of x = 180
⇒
⇒ x =
Hence, maximum marks = 500
Page No 151:
Question 15:
Fill in the blanks.
(i) 3 : 4 = (......)%
(ii) 0.75 = (......)%
(iii) 6% = ...... (express in decimals)
(iv) If x decreased by 40% gives 135, then x = ...... .
(v) (11% of x) − (7% of x) = 18 ⇨ x = ......
Answer:
We have the following:
(i) 3 : 4 = (75)%
Explanation: 3 : 4 = =
(ii) 0.75 = (75)%
Explanation: ( 0.75 100)% = 75%
(iii) 6% = 0.06 (expressed in decimals)
Explanation: 6% =
(iv) If x decreased by 40% gives 135, then x = 225
Explanation:
Let the number be x.
According to question, we have:
x − 40% of x = 135
⇒
⇒
⇒
⇒ x = = 225
(v) (11% of x) − (7% of x) = 18
⇒ x = 450
Explanation:
(11% of x) − (7% of x) = 18
⇒
⇒
∴ x =
Page No 151:
Question 16:
Write 'T' for true and 'F' for false
(i) as rate per cent is 75%
(ii) expressed as a fraction is
(iii) 2 : 5 = 25%
(iv) 80 % of 450 = 360.
(v) 20% of 1 litre = 200 mL.
Answer:
(i) True (T)
Justification: = 75%
(ii) True (T)
Justification: =
(iii) False (F)
Justification: = % = = 40%
(iv) True (T)
Justification: 80% of 450 =
(v) True (T)
Justification: 20% of 1 L = 20% of 1000 mL
= mL = 200 mL
View NCERT Solutions for all chapters of Class 7