# Given below are two quantities named A and B. Based on the given information, you have to determine the relationship between the two quantities. You s

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Given below are two quantities named A and B. Based on the given information, you have to determine the relationship between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.

Quantity A: 28 boys and 7 men can do a piece of work in 4 days and 21 boys and 3 men can do the same work in 7 days. Find the number of days in which 12 boys can complete the work?

Quantity B: 21.5 days

1. Quantity A > Quantity B
2. Quantity A < Quantity B
3. Quantity A ≥ Quantity B
4. Quantity A ≤ Quantity B
5. Quantity A = Quantity B or No relation

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Correct Answer - Option 2 : Quantity A < Quantity B

GIVEN:

(28 boys + 7 men)'s time = 4 days

(21 boys + 3 men)'s time = 7 days

FORMULA USED:
Work = efficiency × time

CALCULATION:

let boy's efficiency be b and man's efficiency be m.

Then, work = (28b + 7m) × 4

Also, work = (21b + 3m) × 7

Equating both the equations,

(28b + 7m) × 4 = (21b + 3m) × 7

⇒ 112b + 28m = 147b + 21m

⇒ 7m = 35b

⇒ m/b = 5/1

∴ Work = (28 × 1 + 7 × 5) × 4 = 252

12 boys' efficiency = 12

12 boys' time = 252/12 = 21 days

∴ Quantity A < Quantity B