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3 men and 5 boys can complete a task in 15 days, whereas 6 men and 7 boys can complete the same task in 9 days. Find the relationship between the task done by the boys and the task done by the men.

3 men and 5 boys can complete a task in 15 days, whereas 6 men and 7 boys can complete the same task in 9 days. Find the relationship between the task done by the boys and the task done by the men. Correct Answer The work of 4 boys is equivalent to the work of 3 men

Let efficiency of 1 man and 1 boy be x and y respectively,

According to the question

(3x + 5y) × 15 = (6x + 7y) × 9

⇒ 45x + 75y = 54x + 63y

⇒ 54x – 45x = 75y – 63y

⇒ 9x = 12y

⇒ x : y = 4 : 3      ----(i)

Let’s check the option

Option 1: 3x = 4y

From (i), we get

3 × 4 = 4 × 3

⇒ 12 = 12

∴ Option 1 is correct 

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