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# RD Sharma (2014) Solutions for Class 7 Math Chapter 11 - Percentage

RD Sharma (2014) Solutions for Class 7 Math Chapter 11 Percentage are provided here with simple step-by-step explanations. These solutions for Percentage are extremely popular among class 7 students for Math Percentage Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the RD Sharma (2014) Book of class 7 Math Chapter 11 are provided here for you for free. You will also love the ad-free experience on Meritnation’s RD Sharma (2014) Solutions. All RD Sharma (2014) Solutions for class 7 Math are prepared by experts and are 100% accurate.

#### Question 1:

Ashu had 24 pages to write. By the evening, he had completed 25% of his work. How many pages were left?

Total number of pages Ashu had to write = 24
Number of pages Ashu completed by the evening = 25% of 24 = (25/100) × 24 = 600/100 = 6
Pages left for completion = 24 - 6 = 18 pages

#### Question 2:

A box contains 60 eggs. Out of which $16\frac{2}{3}%$ are rotten ones. How many eggs are rotten?

Total eggs in the bag = 60
Rotten eggs =

#### Question 3:

Rohit obtained 45 marks out of 80. What per cent marks did he get.

Marks obtained by Rohit = 45/80
Percentage of marks that Rohit obtained = (45/80) × 100 = $\frac{45}{80}×100=\frac{45×100}{80}=\frac{450}{8}=\frac{225}{4}=56\frac{1}{4}$

#### Question 4:

Mr Virmani saves 12% of his salary. If he receives Rs 15900 per month as salary, find his monthly expenditure.

Mr. Virmani's salary = Rs. 15900 per month
Mr. Virmani's savings = 12% of Rs. 15900 = (12/100) × 15900 = Rs. 1908
Mr. Virmani's monthly expenditure = Rs. (15900 - 1908) = Rs. 13992

#### Question 5:

A lawyer willed his 3 sons Rs 250000 to be divided into portions 30%, 45% and 25%. How much did each of them inherit?

Total amount with the lawyer = Rs. 250000
First son's inheritance = 30% of 250000 = (30/100) × 250000 = 7500000/100 = Rs. 75000
Second son's inheritance = 45% of 250000 = (45/1000)​ × 250000 = 11250000/100 = Rs. 112500
Third son's inheritance = 25% of 250000 = (25/100)​ × 250000 = 6250000/100 = Rs. 62500

#### Question 6:

Rajdhani College has 2400 students, 40% of whom are girls. How many boys are there inthe college?

Total number of students in Rajdhani College = 2400
Number of girls = 40%  of 2400 = (40/100) × 2400 = 96000/100 = 960
Number of boys = 2400 - 960 = 1440 boys

#### Question 7:

Aman obtained 410 marks out of 500 in CBSE XII examination while his brother Anish gets 536 marks out of 600 in IX class examination. Find whose performance is better?

Aman's marks in CBSE XII = 410/500
Percentage of marks obtained by Aman = (410/500) ​× ​ 100 = 82

Anish's marks in CBSE IX = 536/600
Percentage of marks obtained by Anish = (536/600)​  ×  100 = 89.33

So, Anish's performance (89.33%) is better than Aman's (82%).

#### Question 8:

Rahim obtained 60 marks out of 75 in Mathematics. Find the percentage of marks obtained by Rahim in Mathematics.

Marks obtained by Rahim in mathematics = 60/75
Percentage of marks obtained by Rahim  = (60/75) × 100 = 80
That is, 80%.

#### Question 9:

In an orchard, $16\frac{2}{3}%$ of the trees are apple trees. If the number of trees in the orchard is 240, find the number of other type of trees in the orchard.

Let the number of apple trees be 'x'.
Number of trees in the orchard = 240
Number of apple trees = $16\frac{2}{3}$% of x
According to the given condition,
$16\frac{2}{3}$% of 240 = x
⇒   ($\frac{50}{3}÷100$) ​​  ×  240 = x
$\frac{50×240}{3×100}$ = x
⇒ x = 40
Number of other types of trees = Total number of trees - number of apple trees = 240 - 40 = 200 trees

#### Question 10:

Ram scored 553 marks out of 700 and Gita scored 486 marks out of 600 in science. Whose performance is better?

Marks scored by Ram = 553/700
Percentage of marks scored by Ram  = (553/700) × 100 = 0.79 × ​100 = 79

Marks scored by Gita = 486/600
Percentage of marks scored by Gita = (486/600) × 100 = 0.81 × 100 = 81

Gita's performance (81%) is better than Ram's (79%).

#### Question 11:

Out of an income of Rs 15000, Nazima spends Rs 10200. What per cent of her income does she save?

Nazima's total income = Rs. 15000
Amount Nazima spends = Rs. 10200
Amount Nazima saves = Rs. (15000 - 10200) = Rs. 4800
Percentage of income Nazima saves = (4800/10200) × 100 = 480000/10200 = 32
Nazima saves 32% of her income.

#### Question 12:

45% of the students in a school are boys. If the total number of students in the school is 880, find the number of girls in the school.

Total number of students in the school = 880
Number of boys in the school = 45% of 880
=  (45/100) × 880
= 39600/100 = 396
Number of girls in the school = 880 - 396 = 484

#### Question 13:

Mr. Sidhana saves 28% of his income. If he saves Rs 840 pr month, find his monthely income.

Let Mr. Sidhana's monthly  income be x.
Monthly savings = Rs. 840
28% of x = Rs. 840
⇒ (28/100)  × x = Rs. 840
⇒ 28x = Rs. 84000
⇒ x = Rs. (84000/28) = Rs. 3000
Mr. Sidhana's monthly income = Rs. 3000

#### Question 14:

In an examination, 8% of the students fail. What percentage of the students pass? If 1650 students appeared in the examination, how many passed?

Total number of students who appeared for the examination = 1650
Number of students who failed = 8% of 1650
= (8/100) ×1650
= (8 × 1650)/100
= 13200/100 = 132
Number of students who passed = 1650 - 132 = 1518
Percentage of students who passed = (1518/1650) × 100 = 0.92 × 100 = 92
That is, 92% of the students passed the examination.

#### Question 15:

In an examination, 9% of the candidates passed and 46 failed. How many candidates appeared?

Let the total number of candidates be x.
Number of candidates who failed = 46
Number of candidates who passed = 92% of
According to the given condition,
92% of x = x - 46
⇒ (92/100) x = x - 46
⇒  92x100x4600
⇒  -8x = - 4600
⇒ x = 4600/8 =
Number of candidates who appeared for the examination = 575

#### Question 1:

Express each of the following per cents as fractions in the simplest forms:
(i) 45%
(ii) 0.25%
(iii) 150%
(iv) $6\frac{1}{4}%$

(i) 45% =  45/100 = 9/20
(ii) 0.25% =  0.25/100 = 25/10000 = 5/2000 = 1/400
(iii) 150% = 150/100 = 15/10 = 3/2
(iv) $6\frac{1}{4}%=\frac{25}{4}÷100=\frac{25}{100×4}=\frac{1}{16}$

#### Question 2:

Express each of the following fractions as a per cent:
(i) $\frac{3}{4}$
(ii) $\frac{53}{100}$
(iii) $1\frac{3}{5}$
(iv) $\frac{7}{20}$

(i) $\left(\frac{3}{4}×100\right)%=75%$
(ii) $\left(\frac{53}{100}×100\right)%=53%$
(iii) $1\frac{3}{5}=\left(\frac{8}{5}×100\right)%=160%$
(iv) $\left(\frac{7}{20}×100\right)%=35%$

#### Question 1:

Express each of the following ratios as per cents:
(i) 4 : 5
(ii) 1 : 5
(iii) 11 : 125

#### Question 2:

Express each of the following per cents as ratios in the simplest forms:
(i) 2.5%
(ii) 0.4%
(iii) $13\frac{3}{4}%$

(i) 2.5% = 2.5/100 = 25/1000 = 5/200 = 1/40
(ii) 0.4% = 0.4/100 = 4/1000 = 1/250
(iii) $13\frac{3}{4}=\frac{55}{4×100}=\frac{11}{80}$

#### Question 1:

Express each of the following per cents as decimals:
(i) 12.5%
(ii) 75%
(iii) 128.8%
(iv) 0.05%

(i) 12.5% = 12.5/100 = 125/1000 = 0.125
(ii) 75% = 75/100 = 0.75
(iii) 128.8% = 128.8/100 = 1288/1000 = 1.288
(iv) 0.05% = 0.05/100 = 5/10000 = 0.0005

#### Question 2:

Express each of the following decimals as a per cent:
(i) 0.004
(ii) 0.24
(iii) 0.02
(iv) 0.275

(i) 0.004 = (0.004 ×  100)% = 0.4%
(ii) 0.24 = (0.24 ×  100 )% =  24%
(iii) 0.02 = (0.02 ×  100)% = 2%
(iv) 0.275 = (0.275 ×  100)% =  27.5%

#### Question 3:

Write each of the following as whole numbers or mixed numbers:
(i) 136%
(ii) 250%
(iii) 300%

(i) 136% = 136/100 = 34/25
(ii) 250% = 250/100 = 5/2
(iii) 300% = 300/100 = 3

#### Question 1:

Find each of the following:
(i) 7% of Rs 7150
(ii) 40% of 400 kg
(iii) 20% of 15.125 litres
(iv)
(v) 2.5% of 600 metres

(i)  7% of  Rs. 7150 = (7/100) ​× 7150 = 50050/100 = Rs.  500.50
(ii) 40% of 400 kg = (40/100) ×  400 = 16000/100 = 160 kg
(iii) 20% of 15.125 litres = (20/100) ×  15.125 =  302.5/100 = 3.025 litres
(iv)
(v) 2.5% of 600 metres = (2.5/100) × 600 = 1500/100 = 15 metres

#### Question 2:

Find the number whose $12\frac{1}{2}%$ is 64.

Let the number be x.

#### Question 3:

What is the number, $6\frac{1}{4}%$ of which is 2?

Let the number be x.

#### Question 4:

If 6 is 50% of a number, what is that number?

Let the number be x.
50% of x = 6
⇒ (50/100) × x = 6
⇒ x = 600/50
⇒ x = 12
So, the number is 12.

#### Question 1:

What per cent of
(i) 24 is 6?
(ii) Rs 125 is Rs 10?
(iii) 4 km is 160 metres?
(iv) Rs 8 is 25 paise
(v) 2 days is 8 hours?
(vi) 1 litre is 175 ml?

Let the number be x.
(i) 24% of x = 6
⇒ (24/100) × x = 6
⇒ x = 600/24 = 25%

(ii) 125% of   = 10
⇒ (125/100) ×  x = 10
⇒ x = 1000/125 = 8%

(iii) 4 km = 4000 metres (1 km = 1000 m)
4000% of  x = 160
⇒ (4000/100) ​× x =  160
⇒  x = 16000/4000  =  4%

(iv) Rs. 8 = 800 paise (Re. 1 = 100 paise)
800%  of x =  25
⇒ (800/ 100) × x = 25
⇒  x = 2500/800 = 25/8 = 3.125%

(v) 2 days = 2 × 24 = 48 (1 day = 24 hours)
48% of x = 8
⇒ (48/100)  ×  x =  8
⇒  x = 800/48 = 100/6 = 16.66%

(vi) 1 litre = 1000 ml
1000% of x = 175
⇒ (1000/100)  × x = 175
⇒ x = 17500/1000 = 175/10 = 17.5%

#### Question 2:

What per cent is equivalent to $\frac{3}{8}$?

Let the percentage equivalent to 3/8 be x.
Then,  x% = $\frac{3}{8}$
⇒ x/100 = $\frac{3}{8}$
⇒ x = $\frac{3×100}{8}=37.5$
Therefore, 3/8 = 37.5%.

#### Question 3:

Find the following:
(i) 8 is 4% of which number?
(ii) 6 is 60% of which number?
(iii) 6 is 30% of which number?
(iv) 12 is 25% of which number?

Let the number be x.

(i) 4% of  = 8
⇒ (4/100) × x = 8
⇒ x = 800/4 = 200

(ii) 60% of x = 6
⇒  (60/100) ×  = 6
⇒   x = 600/60 = 10

(iii) 30% of x = 6
⇒ (30/100) × x = 6
⇒ x = 600/30 = 20

(iv) 25% of  x = 12
⇒ (25/100) × x = 12
⇒   x = 1200/25 = 48

#### Question 4:

Convert each of the following pairs into percentages and find out which is more?
(i) 25 marks out of 30, 35 marks out of 40.
(ii) 100 runs scored off 110 balls, 50 runs scored off 55 balls.

(i) 25 marks out of 30
⇒ (25/30) × 100 = 2500/30 = 83.33%
35 marks out of  40
⇒ (35/40) × 100 = 3500/40 = 87.5%
87.5% is greater than 83.33%.

(ii) 100 runs scored off 110 balls
⇒ (100/110) × 100 = 10000/110 = 90.90%
50  runs scored off  55 balls
⇒ (50/55) × 100 = 5000/55 = 90.90%
Both percentages are equal.

#### Question 5:

Find 20% more than Rs 200.

20% more than 200 means 20% of 200 plus 200.
That is, {(20/100) × 200} + 200 = (4000/100) + 200 = 40 + 200 = 240.

#### Question 6:

Find 10% less than Rs 150.