Aptitude - Ratio and Proportion
21.
If 13 A = 14 B = 15 C, then A : B : C = ?
Answer
Let 13 A = 14 B = 15 C = k, Then A = 3k, B = 4k and C = 5k
∴ A : B : C = 3k : 4k : 5k = 3 : 4 : 5
Answer :
Option AExplanation :
Let 13 A = 14 B = 15 C = k, Then A = 3k, B = 4k and C = 5k
∴ A : B : C = 3k : 4k : 5k = 3 : 4 : 5
22.
If A exceeds B by 40% and B is less than C by 20%, then A : C = ?
Answer
B = 80% of C = 80100 x C = 4C5
A = 140% of B = 140100 x B = 7B5
A = 7B5 = 75 x 4C5 = 28C25
⇒ AC = 2825
∴ A : C = 28 : 25
Answer :
Option DExplanation :
B = 80% of C = 80100 x C = 4C5
A = 140% of B = 140100 x B = 7B5
A = 7B5 = 75 x 4C5 = 28C25
⇒ AC = 2825
∴ A : C = 28 : 25
23.
If y varies directly as (x + 3) and y = 8 when x = 1. What is the value of y when x = 2 ?
Answer
Let y = k(x + 3), where k is a constant.
∴ k(1 + 3) = 8 ⇒ 4k = 8 ⇒ k = 2
∴ y = 2(x + 3)
Thus x = 2 ∴ y = 2(2 + 3) = 10
Answer :
Option BExplanation :
Let y = k(x + 3), where k is a constant.
∴ k(1 + 3) = 8 ⇒ 4k = 8 ⇒ k = 2
∴ y = 2(x + 3)
Thus x = 2 ∴ y = 2(2 + 3) = 10
24.
A right cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is :
Answer
Let the height of the cylinder be h and that of the cone be H. Let the radius of each be r. Then, πr2h = 13πr2H ⇒ hH = 13
So, their heights are in the ratio 1 : 3
Answer :
Option DExplanation :
Let the height of the cylinder be h and that of the cone be H. Let the radius of each be r. Then, πr2h = 13πr2H ⇒ hH = 13
So, their heights are in the ratio 1 : 3
25.
A man had some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens is :
Answer
Let the required number of hens be x. Then, the number of cows = (48 − x)
Then, 2x + 4(48 − x) = 140 ⇒ 2x = (192 − 140) = 52 ⇒ x = 26
Number of hens = 26
Answer :
Option DExplanation :
Let the required number of hens be x. Then, the number of cows = (48 − x)
Then, 2x + 4(48 − x) = 140 ⇒ 2x = (192 − 140) = 52 ⇒ x = 26
Number of hens = 26
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