Question

Direction: Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose among the possible answers.

Quantity I: Average of a, b, c, and d is 5. a is twice of b. b is half of c and d is 5. Find the sum of a and c.

Quantity II: Sum of b, c, and d is 42. c is twice of d and d is 12. Find the sum of b and d.
1. Quantity I ≥ Quantity II
2. Quantity I = Quantity II
3. Quantity I ≤ Quantity II
4. Quantity I ˃ Quantity II
5. Quantity I ˂ Quantity II

Answer 1

Correct Answer - Option 5 : Quantity I ˂ Quantity II

Quantity I:

d = 5

b = c/2

a = 2 × b = 2c/2 = c

According to the question,

(a + b + c + d)/4 = 5

⇒ a + b + c + d = 20

⇒ [c + (c/2)] + c + 5 = 20

⇒ (3c/2) + c + 5 = 20

⇒ 5c/2 = 15

⇒ 5c = 30

⇒ c = 6

⇒ a = 2 × (6/2)

⇒ a = 6

Sum of a and c = 6 + 6 = 12

Quantity II:

Sum of b, c and d = 42

c = 2d, d = 12

⇒ b + 2d + 12 = 42

⇒ b + 2(12) + 12 = 42

⇒ b + 24 + 12 = 42

⇒ b + 36 = 42

⇒ b = 6

Sum of b and d = 6 + 12 = 18

∴ Quantity I ˂ Quantity II