RS Aggarwal 2020 2021 Solutions for Class 7 Maths Chapter 8 Ratio And Proportion are provided here with simple step-by-step explanations. These solutions for Ratio And Proportion are extremely popular among class 7 students for Maths Ratio And Proportion Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the RS Aggarwal 2020 2021 Book of class 7 Maths Chapter 8 are provided here for you for free. You will also love the ad-free experience on Meritnation’s RS Aggarwal 2020 2021 Solutions. All RS Aggarwal 2020 2021 Solutions for class 7 Maths are prepared by experts and are 100% accurate.
Page No 124:
Question 1:
Answer:
(i) HCF of 24 and 40 is 8.
∴ 24 : 40 = = 3 : 5
Hence, 24 : 40 in its simplest form is 3 : 5.
(ii) HCF of 13.5 and 15 is 1.5.
Hence, 13.5 : 15 in its simplest form is 9 : 10.
(iii)
The HCF of 40 and 45 is 5.
∴ 40 : 45 = = 8 : 9
Hence, in its simplest form is 8 : 9
(iv) 9 : 6
The HCF of 9 and 6 is 3.
Hence, in its simplest form is 3 : 2.
(v) LCM of the denominators is 2.
The HCF of these 3 numbers is 1.
∴ 8 : 10 : 9 is the simplest form.
(vi) 2.5 : 6.5 : 8 = 25 : 65 : 80
The HCF of 25, 65 and 80 is 5.
∴ 25 : 65 : 80 = = 5 : 13 : 16
Page No 124:
Question 2:
(i) HCF of 24 and 40 is 8.
∴ 24 : 40 = = 3 : 5
Hence, 24 : 40 in its simplest form is 3 : 5.
(ii) HCF of 13.5 and 15 is 1.5.
Hence, 13.5 : 15 in its simplest form is 9 : 10.
(iii)
The HCF of 40 and 45 is 5.
∴ 40 : 45 = = 8 : 9
Hence, in its simplest form is 8 : 9
(iv) 9 : 6
The HCF of 9 and 6 is 3.
Hence, in its simplest form is 3 : 2.
(v) LCM of the denominators is 2.
The HCF of these 3 numbers is 1.
∴ 8 : 10 : 9 is the simplest form.
(vi) 2.5 : 6.5 : 8 = 25 : 65 : 80
The HCF of 25, 65 and 80 is 5.
∴ 25 : 65 : 80 = = 5 : 13 : 16
Answer:
(i) Converting both the quantities into the same unit, we have:
75 paise : (3 100) paise = 75 : 300
= (âµ HCF of 75 and 300 = 75)
= 1 paise : 4 paise
(ii) Converting both the quantities into the same unit, we have:
105 cm : 63 cm = (âµ HCF of 105 and 63 = 21)
= 5 cm : 3 cm
(iii) Converting both the quantities into the same unit
65 min : 45 min = (âµ HCF of 65 and 45 = 5)
= 13 min : 9 min
(iv) Converting both the quantities into the same unit, we get:
8 months : 12 months = (âµ HCF of 8 and 12 = 4)
= 2 months : 3 months
(v) Converting both the quantities into the same unit, we get:
2250g : 3000 g = (âµ HCF of 2250 and 3000 = 750)
= 3 g : 4 g
(vi) Converting both the quantities into the same unit, we get:
1000 m : 750 m = (âµ HCF of 1000 and 750 = 250)
= 4 m : 3 m
Page No 124:
Question 3:
(i) Converting both the quantities into the same unit, we have:
75 paise : (3 100) paise = 75 : 300
= (âµ HCF of 75 and 300 = 75)
= 1 paise : 4 paise
(ii) Converting both the quantities into the same unit, we have:
105 cm : 63 cm = (âµ HCF of 105 and 63 = 21)
= 5 cm : 3 cm
(iii) Converting both the quantities into the same unit
65 min : 45 min = (âµ HCF of 65 and 45 = 5)
= 13 min : 9 min
(iv) Converting both the quantities into the same unit, we get:
8 months : 12 months = (âµ HCF of 8 and 12 = 4)
= 2 months : 3 months
(v) Converting both the quantities into the same unit, we get:
2250g : 3000 g = (âµ HCF of 2250 and 3000 = 750)
= 3 g : 4 g
(vi) Converting both the quantities into the same unit, we get:
1000 m : 750 m = (âµ HCF of 1000 and 750 = 250)
= 4 m : 3 m
Answer:
Therefore, we have:
∴ A : C = 9 : 10
Page No 124:
Question 4:
Therefore, we have:
∴ A : C = 9 : 10
Answer:
∴ A : C = 2 : 5
Page No 124:
Question 5:
∴ A : C = 2 : 5
Answer:
A : B = 3 : 5
B : C = 10 : 13 =
Now, A : B : C = 3 : 5 :
∴ A : B : C = 6 : 10 : 13
Page No 124:
Question 6:
A : B = 3 : 5
B : C = 10 : 13 =
Now, A : B : C = 3 : 5 :
∴ A : B : C = 6 : 10 : 13
Answer:
We have the following:
A : B = 5 : 6
B : C = 4 : 7 =
∴ A : B : C = 5 : 6 : = 10 : 12 : 21
Page No 124:
Question 7:
We have the following:
A : B = 5 : 6
B : C = 4 : 7 =
∴ A : B : C = 5 : 6 : = 10 : 12 : 21
Answer:
Sum of the ratio terms = 7 + 8 = 15
Now, we have the following:
Kunal's share = Rs 360 = Rs 168
Mohit's share = Rs 360 = Rs 192
Page No 125:
Question 8:
Sum of the ratio terms = 7 + 8 = 15
Now, we have the following:
Kunal's share = Rs 360 = Rs 168
Mohit's share = Rs 360 = Rs 192
Answer:
Sum of the ratio terms =
Now, we have the following:
Rajan's share = Rs 880 = Rs 480
Kamal's share = Rs 880 = Rs 400
Page No 125:
Question 9:
Sum of the ratio terms =
Now, we have the following:
Rajan's share = Rs 880 = Rs 480
Kamal's share = Rs 880 = Rs 400
Answer:
Sum of the ratio terms is (1 + 3 + 4) = 8
We have the following:
A's share = Rs 5600
B's share = Rs 5600 = Rs 2100
C's share = Rs 5600 = Rs 2800
Page No 125:
Question 10:
Sum of the ratio terms is (1 + 3 + 4) = 8
We have the following:
A's share = Rs 5600
B's share = Rs 5600 = Rs 2100
C's share = Rs 5600 = Rs 2800
Answer:
Let x be the required number.
Then, (9 + x) : (16 + x) = 2 : 3
Hence, 5 must be added to each term of the ratio 9 : 16 to make it 2 : 3.
Page No 125:
Question 11:
Let x be the required number.
Then, (9 + x) : (16 + x) = 2 : 3
Hence, 5 must be added to each term of the ratio 9 : 16 to make it 2 : 3.
Answer:
Suppose that x is the number that must be subtracted.
Then, (17 − x) : (33 − x) = 7 : 15
Hence, 3 must be subtracted from each term of ratio 17 : 33 so that it becomes 7 : 15.
Page No 125:
Question 12:
Suppose that x is the number that must be subtracted.
Then, (17 − x) : (33 − x) = 7 : 15
Hence, 3 must be subtracted from each term of ratio 17 : 33 so that it becomes 7 : 15.
Answer:
Suppose that the numbers are 7x and 11x.
Then, (7x + 7) : (11x + 7) = 2 : 3
⇒
⇒ 21x + 21 = 22x + 14
⇒ x = 7
Hence, the numbers are (7 7 =) 49 and (11 7 =) 77.
Page No 125:
Question 13:
Suppose that the numbers are 7x and 11x.
Then, (7x + 7) : (11x + 7) = 2 : 3
⇒
⇒ 21x + 21 = 22x + 14
⇒ x = 7
Hence, the numbers are (7 7 =) 49 and (11 7 =) 77.
Answer:
Suppose that the numbers are 5x and 9x.
Then, (5x − 3) : (9x − 3) = 1 : 2
⇒
⇒ 10x − 6 = 9x − 3
⇒ x = 3
Hence, the numbers are (5 3 =) 15 and (9 3 =) 27.
Page No 125:
Question 14:
Suppose that the numbers are 5x and 9x.
Then, (5x − 3) : (9x − 3) = 1 : 2
⇒
⇒ 10x − 6 = 9x − 3
⇒ x = 3
Hence, the numbers are (5 3 =) 15 and (9 3 =) 27.
Answer:
Let the numbers be 3x and 4x.
Their LCM is 12x.
Then, 12x = 180
⇒ x = 15
∴ The numbers are (3 15 =) 45 and (4 15 =) 60.
Page No 125:
Question 15:
Let the numbers be 3x and 4x.
Their LCM is 12x.
Then, 12x = 180
⇒ x = 15
∴ The numbers are (3 15 =) 45 and (4 15 =) 60.
Answer:
Suppose that the present ages of A and B are 8x yrs and 3x yrs.
Then, (8x + 6) : (3x + 6) = 9 : 4
⇒
⇒ 32x + 24 = 27x + 54
⇒ 5x = 30
⇒ x = 6
Now, present age of A = 8 6 yrs = 48 yrs
Present age of B = 3 6 yrs = 18 yrs
Page No 125:
Question 16:
Suppose that the present ages of A and B are 8x yrs and 3x yrs.
Then, (8x + 6) : (3x + 6) = 9 : 4
⇒
⇒ 32x + 24 = 27x + 54
⇒ 5x = 30
⇒ x = 6
Now, present age of A = 8 6 yrs = 48 yrs
Present age of B = 3 6 yrs = 18 yrs
Answer:
Suppose that the weight of zinc is x g.
Then, 48.6 : x = 9 : 5
⇒ x = = 27
Hence, the weight of zinc in the alloy is 27 g.
Page No 125:
Question 17:
Suppose that the weight of zinc is x g.
Then, 48.6 : x = 9 : 5
⇒ x = = 27
Hence, the weight of zinc in the alloy is 27 g.
Answer:
Suppose that the number of boys is x.
Then, x : 375 = 8 : 3
⇒ x = = 1000
Hence, the number of girls in the school is 1000.
Page No 125:
Question 18:
Suppose that the number of boys is x.
Then, x : 375 = 8 : 3
⇒ x = = 1000
Hence, the number of girls in the school is 1000.
Answer:
Suppose that the monthly income of the family is Rs x.
Then, x : 2500 = 11 : 2
⇒ x =
⇒ x = Rs 13750
Hence, the income is Rs 13,750.
∴ Expenditure = (monthly income − savings)
=Rs (13750 − 2500)
= Rs 11250
Page No 125:
Question 19:
Suppose that the monthly income of the family is Rs x.
Then, x : 2500 = 11 : 2
⇒ x =
⇒ x = Rs 13750
Hence, the income is Rs 13,750.
∴ Expenditure = (monthly income − savings)
=Rs (13750 − 2500)
= Rs 11250
Answer:
Let the numbers one rupee, fifty paise and twenty-five paise coins be 5x, 8x and 4x, respectively.
Total value of these coins = ()
However, the total value is Rs 750.
∴ 750 = 10x
⇒ x = 75
Hence, number of one rupee coins = 5 75 = 375
Number of fifty paise coins = 8 75 = 600
Number of twenty-five paise coins = 4 75 = 300
Page No 125:
Question 20:
Let the numbers one rupee, fifty paise and twenty-five paise coins be 5x, 8x and 4x, respectively.
Total value of these coins = ()
However, the total value is Rs 750.
∴ 750 = 10x
⇒ x = 75
Hence, number of one rupee coins = 5 75 = 375
Number of fifty paise coins = 8 75 = 600
Number of twenty-five paise coins = 4 75 = 300
Answer:
(4x + 5) : (3x + 11) = 13 : 17
Page No 125:
Question 21:
(4x + 5) : (3x + 11) = 13 : 17
Answer:
Now, we have (3x + 4y) : (5x + 6y)
= 25 : 39
Page No 125:
Question 22:
Now, we have (3x + 4y) : (5x + 6y)
= 25 : 39
Answer:
Now, we have:
∴ (8x − 3y) : (3x + 2y) = 3 : 8
Page No 125:
Question 23:
Now, we have:
∴ (8x − 3y) : (3x + 2y) = 3 : 8
Answer:
Suppose that the numbers are 5x and 7x.
The sum of the numbers is 720.
i.e., 5x + 7x = 720
⇒ 12x = 720
⇒ x = 60
Hence, the numbers are (5 60 =) 300 and (7 60 =) 420.
Page No 125:
Question 24:
Suppose that the numbers are 5x and 7x.
The sum of the numbers is 720.
i.e., 5x + 7x = 720
⇒ 12x = 720
⇒ x = 60
Hence, the numbers are (5 60 =) 300 and (7 60 =) 420.
Answer:
(i) The LCM of 6 and 9 is 18.
∴ (7 : 9) (5 : 6)
(ii) The LCM of 3 and 7 is 21.
∴ (4 : 7) (2 : 3)
(iii) The LCM of 2 and 7 is 14.
Clearly,
∴ (1 : 2) (4 : 7)
(iv) The LCM of 5 and 13 is 65.
∴ (3 : 5) (8 : 13)
Page No 125:
Question 25:
(i) The LCM of 6 and 9 is 18.
∴ (7 : 9) (5 : 6)
(ii) The LCM of 3 and 7 is 21.
∴ (4 : 7) (2 : 3)
(iii) The LCM of 2 and 7 is 14.
Clearly,
∴ (1 : 2) (4 : 7)
(iv) The LCM of 5 and 13 is 65.
∴ (3 : 5) (8 : 13)
Answer:
(i) We have
The LCM of 6, 9 and 18 is 18. Therefore, we have:
Hence, (11 : 18) (5 : 6) (8 : 9)
(ii)
The LCM of 14, 21, 7 and 3 is 42.
Page No 128:
Question 1:
(i) We have
The LCM of 6, 9 and 18 is 18. Therefore, we have:
Hence, (11 : 18) (5 : 6) (8 : 9)
(ii)
The LCM of 14, 21, 7 and 3 is 42.
Answer:
We have:
Product of the extremes = 30 60 = 1800
Product of the means = 40 45 = 1800
Product of extremes = Product of means
Hence, 30 : 40 :: 45 : 60
Page No 128:
Question 2:
We have:
Product of the extremes = 30 60 = 1800
Product of the means = 40 45 = 1800
Product of extremes = Product of means
Hence, 30 : 40 :: 45 : 60
Answer:
We have:
Product of the extremes = 36 7 = 252
Product of the means = 49 6 = 294
Product of the extremes Product of the means
Hence, 36, 49, 6 and 7 are not in proportion.
Page No 128:
Question 3:
We have:
Product of the extremes = 36 7 = 252
Product of the means = 49 6 = 294
Product of the extremes Product of the means
Hence, 36, 49, 6 and 7 are not in proportion.
Answer:
Product of the extremes = 2 27 = 54
Product of the means = 9 x = 9x
Since 2 : 9 :: x : 27, we have:
Product of the extremes = Product of the means
⇒ 54 = 9x
⇒ x = 6
Page No 128:
Question 4:
Product of the extremes = 2 27 = 54
Product of the means = 9 x = 9x
Since 2 : 9 :: x : 27, we have:
Product of the extremes = Product of the means
⇒ 54 = 9x
⇒ x = 6
Answer:
Product of the extremes = 8 35 = 280
Product of the means = 16 x = 16x
Since 8 : x :: 16 : 35, we have:
Product of the extremes = Product of the means
⇒ 280 = 16x
⇒ x = 17.5
Page No 128:
Question 5:
Product of the extremes = 8 35 = 280
Product of the means = 16 x = 16x
Since 8 : x :: 16 : 35, we have:
Product of the extremes = Product of the means
⇒ 280 = 16x
⇒ x = 17.5
Answer:
Product of the extremes = x 60 = 60x
Product of the means = 35 48 = 1680
Since x : 35 :: 48 : 60, we have:
Product of the extremes = Product of the means
⇒ 60x= 1680
⇒ x = 28
Page No 128:
Question 6:
Product of the extremes = x 60 = 60x
Product of the means = 35 48 = 1680
Since x : 35 :: 48 : 60, we have:
Product of the extremes = Product of the means
⇒ 60x= 1680
⇒ x = 28
Answer:
(i) Let the fourth proportional be x.
Then, 8 : 36 :: 6 : x
8 [Product of extremes = Product of means]
⇒ 8x = 216
⇒ x = 27
Hence, the fourth proportional is 27.
(ii) Let the fourth proportional be x.
Then, 5 : 7 :: 30 : x
⇒ [Product of extremes = Product of means]
⇒ 8x = 216
⇒ 5x = 210
⇒ x = 42
Hence, the fourth proportional is 42.
(iii) Let the fourth proportional be x.
Then, 2.8 [Product of extremes = Product of means]
⇒ 8x = 216
⇒ 2.8x = 49
⇒ x = 17.5
Hence, the fourth proportional is 17.5.
Page No 128:
Question 7:
(i) Let the fourth proportional be x.
Then, 8 : 36 :: 6 : x
8 [Product of extremes = Product of means]
⇒ 8x = 216
⇒ x = 27
Hence, the fourth proportional is 27.
(ii) Let the fourth proportional be x.
Then, 5 : 7 :: 30 : x
⇒ [Product of extremes = Product of means]
⇒ 8x = 216
⇒ 5x = 210
⇒ x = 42
Hence, the fourth proportional is 42.
(iii) Let the fourth proportional be x.
Then, 2.8 [Product of extremes = Product of means]
⇒ 8x = 216
⇒ 2.8x = 49
⇒ x = 17.5
Hence, the fourth proportional is 17.5.
Answer:
36, 54 and x are in continued proportion.
Then, 36 : 54 :: 54 : x
⇒ [Product of extremes = Product of means]
⇒ 36x = 2916
⇒ x = 81
Page No 128:
Question 8:
36, 54 and x are in continued proportion.
Then, 36 : 54 :: 54 : x
⇒ [Product of extremes = Product of means]
⇒ 36x = 2916
⇒ x = 81
Answer:
27, 36 and x are in continued proportion.
Then, 27 : 36 :: 36 : x
⇒ [Product of extremes = Product of means]
⇒ 27x = 1296
⇒ x = 48
Hence, the value of x is 48.
Page No 128:
Question 9:
27, 36 and x are in continued proportion.
Then, 27 : 36 :: 36 : x
⇒ [Product of extremes = Product of means]
⇒ 27x = 1296
⇒ x = 48
Hence, the value of x is 48.
Answer:
(i) Suppose that x is the third proportional to 8 and 12.
Then, 8 :12 :: 12 : x
⇒ 8 (Product of extremes = Product of means )
⇒ 8x = 144
⇒ x = 18
Hence, the required third proportional is 18.
(ii) Suppose that x is the third proportional to 12 and 18.
Then, 12 : 18 :: 18 : x
⇒ (Product of extremes = Product of means )
⇒ 12x = 324
⇒ x = 27
Hence, the third proportional is 27.
(iii) Suppose that x is the third proportional to 4.5 and 6.
Then, 4.5 : 6:: 6 : x
⇒ (Product of extremes = Product of means )
⇒ 4.5x = 36
⇒ x = 8
Hence, the third proportional is 8.
Page No 128:
Question 10:
(i) Suppose that x is the third proportional to 8 and 12.
Then, 8 :12 :: 12 : x
⇒ 8 (Product of extremes = Product of means )
⇒ 8x = 144
⇒ x = 18
Hence, the required third proportional is 18.
(ii) Suppose that x is the third proportional to 12 and 18.
Then, 12 : 18 :: 18 : x
⇒ (Product of extremes = Product of means )
⇒ 12x = 324
⇒ x = 27
Hence, the third proportional is 27.
(iii) Suppose that x is the third proportional to 4.5 and 6.
Then, 4.5 : 6:: 6 : x
⇒ (Product of extremes = Product of means )
⇒ 4.5x = 36
⇒ x = 8
Hence, the third proportional is 8.
Answer:
The third proportional to 7 and x is 28.
Then, 7 : x :: x : 28
⇒ 7 28 = (Product of extremes = Product of means)
⇒ x = 14
Page No 128:
Question 11:
The third proportional to 7 and x is 28.
Then, 7 : x :: x : 28
⇒ 7 28 = (Product of extremes = Product of means)
⇒ x = 14
Answer:
(i) Suppose that x is the mean proportional.
Then, 6 : x :: x : 24
⇒ (Product of extremes = Product of means)
⇒
⇒ x = 12
Hence, the mean proportional to 6 and 24 is 12.
(ii) Suppose that x is the mean proportional.
Then, 3 : x :: x : 27
(Product of extremes =Product of means)
⇒ x = 9
Hence, the mean proportional to 3 and 27 is 9.
(iii) Suppose that x is the mean proportional.
Then, 0.4 : x :: x : 0.9
(Product of extremes =Product of means)
⇒x = 0.6
Hence, the mean proportional to 0.4 and 0.9 is 0.6.
Page No 128:
Question 12:
(i) Suppose that x is the mean proportional.
Then, 6 : x :: x : 24
⇒ (Product of extremes = Product of means)
⇒
⇒ x = 12
Hence, the mean proportional to 6 and 24 is 12.
(ii) Suppose that x is the mean proportional.
Then, 3 : x :: x : 27
(Product of extremes =Product of means)
⇒ x = 9
Hence, the mean proportional to 3 and 27 is 9.
(iii) Suppose that x is the mean proportional.
Then, 0.4 : x :: x : 0.9
(Product of extremes =Product of means)
⇒x = 0.6
Hence, the mean proportional to 0.4 and 0.9 is 0.6.
Answer:
Suppose that the number is x.
Then, (5 + x) : ( 9 + x) :: (7 + x) : (12 + x)
Hence, 3 must be added to each of the numbers: 5, 9, 7 and 12, to get the numbers which are in proportion.
Page No 128:
Question 13:
Suppose that the number is x.
Then, (5 + x) : ( 9 + x) :: (7 + x) : (12 + x)
Hence, 3 must be added to each of the numbers: 5, 9, 7 and 12, to get the numbers which are in proportion.
Answer:
Suppose that x is the number that is to be subtracted.
Then, (10 − x) : (12 − x) :: (19 − x) : (24 − x)
.
Hence, 4 must be subtracted from each of the numbers: 10, 12, 19 and 24, to get the numbers which are in proportion.
Page No 128:
Question 14:
Suppose that x is the number that is to be subtracted.
Then, (10 − x) : (12 − x) :: (19 − x) : (24 − x)
.
Hence, 4 must be subtracted from each of the numbers: 10, 12, 19 and 24, to get the numbers which are in proportion.
Answer:
Distance represented by 1 cm on the map = 5000000 cm = 50 km
Distance represented by 3 cm on the map = 50 4 km = 200 km
∴ The actual distance is 200 km.
Page No 128:
Question 15:
Distance represented by 1 cm on the map = 5000000 cm = 50 km
Distance represented by 3 cm on the map = 50 4 km = 200 km
∴ The actual distance is 200 km.
Answer:
(Height of tree) : (height of its shadow) = (height of the pole) : (height of its shadow)
Suppose that the height of pole is x cm.
Then, 6 : 8 = x : 20
⇒ x =
∴ Height of the pole = 15 cm
Page No 128:
Question 1:
(Height of tree) : (height of its shadow) = (height of the pole) : (height of its shadow)
Suppose that the height of pole is x cm.
Then, 6 : 8 = x : 20
⇒ x =
∴ Height of the pole = 15 cm
Answer:
The correct option is (d).
Hence, a : c = 2 : 3
Page No 128:
Question 2:
The correct option is (d).
Hence, a : c = 2 : 3
Answer:
(a) 15 : 8
Page No 128:
Question 3:
(a) 15 : 8
Answer:
The correct option is (d).
Hence, A : C = 15 : 8
Page No 128:
Question 4:
The correct option is (d).
Hence, A : C = 15 : 8
Answer:
The correct option is (b).
Hence, A : B = 4 : 3
Page No 128:
Question 5:
The correct option is (b).
Hence, A : B = 4 : 3
Answer:
(a) 1 : 3 : 6
Page No 129:
Question 6:
(a) 1 : 3 : 6
Answer:
(b) 30 : 42 : 77
Page No 129:
Question 7:
(b) 30 : 42 : 77
Answer:
(c) 6 : 4 : 3
Page No 129:
Question 8:
(c) 6 : 4 : 3
Answer:
(a) 3 : 4 : 5
= 3 : 4 : 5
Page No 129:
Question 9:
(a) 3 : 4 : 5
= 3 : 4 : 5
Answer:
(b) 15 : 10 : 6
Page No 129:
Question 10:
(b) 15 : 10 : 6
Answer:
Hence, (7x + 3y) : (7x − 3y) = 11 : 3
The correct option is (c).
Page No 129:
Question 11:
Hence, (7x + 3y) : (7x − 3y) = 11 : 3
The correct option is (c).
Answer:
(c) 5 : 2
∴ a : b = 5 : 2
Page No 129:
Question 12:
(c) 5 : 2
∴ a : b = 5 : 2
Answer:
(c) 9
Page No 129:
Question 13:
(c) 9
Answer:
(b) 7
Suppose that x is the number that is to be added.
Then, (3 + x) : (5 + x) = 5 : 6
Page No 129:
Question 14:
(b) 7
Suppose that x is the number that is to be added.
Then, (3 + x) : (5 + x) = 5 : 6
Answer:
(d) 40
Suppose that the numbers are x and y.
Then, x : y = 3 : 5 and (x + 10) : (y + 10) = 5 : 7
Hence, sum of numbers = 15 + 25 = 40
Page No 129:
Question 15:
(d) 40
Suppose that the numbers are x and y.
Then, x : y = 3 : 5 and (x + 10) : (y + 10) = 5 : 7
Hence, sum of numbers = 15 + 25 = 40
Answer:
(a) 3
Suppose that x is the number that is to be subtracted.
Then, (15 − x) : (19 − x) = 3 : 4
Page No 129:
Question 16:
(a) 3
Suppose that x is the number that is to be subtracted.
Then, (15 − x) : (19 − x) = 3 : 4
Answer:
(a) Rs 180
A's share =
Page No 129:
Question 17:
(a) Rs 180
A's share =
Answer:
(d) 416
Let x be the number of boys.
Then, 8 : 5 = x : 160
Page No 129:
Question 18:
(d) 416
Let x be the number of boys.
Then, 8 : 5 = x : 160
Answer:
(a) (2 :3)
LCM of 3 and 7 = 21
Page No 129:
Question 19:
(a) (2 :3)
LCM of 3 and 7 = 21
Answer:
(c) 16
Suppose that the third proportional is x.
Then, 9 : 12 :: 12 : x
Page No 129:
Question 20:
(c) 16
Suppose that the third proportional is x.
Then, 9 : 12 :: 12 : x
Answer:
(b) 12
Suppose that the mean proportional is x.
Then, 9 : x :: x : 16
Page No 129:
Question 21:
(b) 12
Suppose that the mean proportional is x.
Then, 9 : x :: x : 16
Answer:
(a) 18 years
Suppose that the present ages of A and B are 3x yrs and 8x yrs, respectively.
After six years, the age of A will be (3x+6) yrs and that of B will be (8x+6) yrs.
Then, (3x +6) : (8x + 6) = 4 : 9
Page No 131:
Question 1:
(a) 18 years
Suppose that the present ages of A and B are 3x yrs and 8x yrs, respectively.
After six years, the age of A will be (3x+6) yrs and that of B will be (8x+6) yrs.
Then, (3x +6) : (8x + 6) = 4 : 9
Answer:
The given fractions are .
LCM of 5 and 9 = 5 9 = 45
Page No 131:
Question 2:
The given fractions are .
LCM of 5 and 9 = 5 9 = 45
Answer:
The sum of ratio terms is 10.
Then, we have:
A's share = Rs
Page No 131:
Question 3:
The sum of ratio terms is 10.
Then, we have:
A's share = Rs
Answer:
Product of the extremes = 25 6 = 150
Product of the means = 36 5 = 180
The product of the extremes is not equal to that of the means.
Hence, 25, 36, 5 and 6 are not in proportion.
Page No 131:
Question 4:
Product of the extremes = 25 6 = 150
Product of the means = 36 5 = 180
The product of the extremes is not equal to that of the means.
Hence, 25, 36, 5 and 6 are not in proportion.
Answer:
x : 18 :: 18 : 108
Page No 131:
Question 5:
x : 18 :: 18 : 108
Answer:
Suppose that the numbers are 5x and 7x.
Then, 5x + 7x = 84
⇒ 12x = 84
⇒ x = 7
Hence, the numbers are (5 7 =) 35 and (7 7 =) 49.
Page No 131:
Question 6:
Suppose that the numbers are 5x and 7x.
Then, 5x + 7x = 84
⇒ 12x = 84
⇒ x = 7
Hence, the numbers are (5 7 =) 35 and (7 7 =) 49.
Answer:
Suppose that the present ages of A and B are 4x yrs and 3x yrs, respectively.
Eight years ago, age of A = (4x − 8) yrs
Eight years ago, age of B = (3x − 8) yrs
Then, (4x − 8) : (3x − 8) = 10 : 7
Page No 131:
Question 7:
Suppose that the present ages of A and B are 4x yrs and 3x yrs, respectively.
Eight years ago, age of A = (4x − 8) yrs
Eight years ago, age of B = (3x − 8) yrs
Then, (4x − 8) : (3x − 8) = 10 : 7
Answer:
Distance covered in 60 min = 54 km
Distance covered in 1 min =
∴ Distance covered in 40 min =
Page No 131:
Question 8:
Distance covered in 60 min = 54 km
Distance covered in 1 min =
∴ Distance covered in 40 min =
Answer:
Suppose that the third proportional to 8 and 12 is x.
Then, 8 : 12 :: 12 : x
⇒ 8x = 144 (Product of extremes = Product of means)
⇒ x = 18
Hence, the third proportional is 18 .
Page No 131:
Question 9:
Suppose that the third proportional to 8 and 12 is x.
Then, 8 : 12 :: 12 : x
⇒ 8x = 144 (Product of extremes = Product of means)
⇒ x = 18
Hence, the third proportional is 18 .
Answer:
40 men can finish the work in 60 days.
1 man can finish the work in 60 40 days. [Less men, more days]
75 men can finish the work in
Hence, 75 men will finish the same work in 32 days.
Page No 131:
Question 10:
40 men can finish the work in 60 days.
1 man can finish the work in 60 40 days. [Less men, more days]
75 men can finish the work in
Hence, 75 men will finish the same work in 32 days.
Answer:
(d) 6 : 4 : 3
Page No 131:
Question 11:
(d) 6 : 4 : 3
Answer:
(a) 2 : 3 : 4
Page No 131:
Question 12:
(a) 2 : 3 : 4
Answer:
(c) 11 : 3
Page No 131:
Question 13:
(c) 11 : 3
Answer:
(a) 3
Suppose that the number to be subtracted is x.
Then, (15 − x) : (19 − x) = 3 : 4
Page No 131:
Question 14:
(a) 3
Suppose that the number to be subtracted is x.
Then, (15 − x) : (19 − x) = 3 : 4
Answer:
(b) 360
Sum of the ratio terms = 4 + 3 = 7
∴ B's share = = Rs 360
Page No 131:
Question 15:
(b) 360
Sum of the ratio terms = 4 + 3 = 7
∴ B's share = = Rs 360
Answer:
(c) 40 years
Suppose that the present ages of A and B are 5x yrs and 2x yrs, respectively.
After 5 years, the ages of A and B will be (5x+5) yrs and (2x+5) yrs, respectively.
Then, (5x + 5) : (2x + 5) = 15 : 7
⇒
Cross multiplying, we get:
35x + 35 = 30x + 75
⇒ 5x = 40
⇒ x = 8
Hence, the present age of A is 5 8 = 40 yrs.
Page No 131:
Question 16:
(c) 40 years
Suppose that the present ages of A and B are 5x yrs and 2x yrs, respectively.
After 5 years, the ages of A and B will be (5x+5) yrs and (2x+5) yrs, respectively.
Then, (5x + 5) : (2x + 5) = 15 : 7
⇒
Cross multiplying, we get:
35x + 35 = 30x + 75
⇒ 5x = 40
⇒ x = 8
Hence, the present age of A is 5 8 = 40 yrs.
Answer:
(b) 896
Suppose that the number of boys in the school is x.
Then, x : 320 = 9 : 5
⇒ 5x = 2880
⇒ x = 576
Hence, total strength of the school = 576 + 320 = 896
Page No 131:
Question 17:
(b) 896
Suppose that the number of boys in the school is x.
Then, x : 320 = 9 : 5
⇒ 5x = 2880
⇒ x = 576
Hence, total strength of the school = 576 + 320 = 896
Answer:
(i) 15 : 8
∴ C : A=15 : 8
(ii) 5 : 4
(iii) 1 : 3 : 6
(iv) 30 : 42 : 77
Page No 131:
Question 18:
(i) 15 : 8
∴ C : A=15 : 8
(ii) 5 : 4
(iii) 1 : 3 : 6
(iv) 30 : 42 : 77
Answer:
(i) F
Suppose that the mean proportional is x.
Then, 0.4 : x :: x : 0.9
(ii) F
Suppose that the third proportional is x.
Then, 9 : 12 :: 12 : x
⇒ 9x = 144 (Product of extremes = Product of means)
⇒ x = 16
(iii) T
8 : x :: 48 : 18
⇒ 144 = 48x (Product of extremes = Product of means)
⇒ x = 3
(iv) T
⇒ 12a = 30b
⇒ a : b = 5 : 2
View NCERT Solutions for all chapters of Class 7