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SSC GD 2023 PYQ — Question 49

SSC GD Constable (English) - 27 Jan 2023 - Shift 3 • Quantitative Aptitude • Q49

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Three men and two women can finish a work in 120/13 days. Two men and three women can finish the same work in 10 days. One man and one woman start the work, and after 12 days, 1 more man joins the work. After three more days, it is directed to engage more men or women to finish the work the next day. How many minimum more men or women must be engaged to complete the work as per the direction?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. Either 14 women or 10 men.

(3M + 2W) × 12013\frac{120}{13} = (2M + 3W) × 10

36M + 24W = 26M + 39W

10M = 15W

M/W = 3/2

Total work =  (2 × 3 + 3 × 2) × 10 = 120 unit

According to the question,

work done by 1 man and 1 woman for 12 days = (1 × 3 + 1 × 2) × 12 = 60 unit

work done by 2 men and 1 woman for 3 days = (2 × 3 + 1 × 2) × 3 = 24 unit

Remaining work = 120 - (60 + 24) = 36 unit

Let's assume X more men joined the group to finish the task in 1 day:

36(2+x)×3+2=1\frac{36}{(2 +x)× 3 + 2}=1

36 = 6 + 3x + 2

x = 28/3 = 9.33 men = 10 men (Approx)

or 

Let's assume Y more women joined the group to finish the task in 1 day:

 362×3+(1+y)×2=1\frac{36}{2 × 3 + (1 +y)× 2}=1

36 = 6 + 2y + 2

y = 28/2 = 14 women

So, minimum either 14 women or 10 men must be engaged to complete the work as per the direction