12 men and 16 boys can do a piece of work in 5 days 13 men and 24 boys can do it in 4 days. The ratio of the daily work done by a man to that of a boy is (A) 2:1 (B) 3:1 (C) 3:2 (D) 5:4

Let us assume

Boy finish the work in x days and man finish the work in y days

So,

One day work of a boy = 1/x and one day work of a man = 1/y

One day work of 16 boys = 16/x and one day work of 12 men = 12/y

Given that,

One day work of 12 men and 16 boys = 1/5

⇒ 16/x + 12/y = 1/5 … (1)

Similarly,

One day work of 13 men and 24 boys = 1/4

24/x + 13/y = 1/4 ….. (2)

Multiplying by 3 to equation (1) and 2 to equation (2)

48/x + 36/y = 3/5 ….. (3)

48/x + 26/y = 2/4 …… (4)

Subtract equation (4) from equation (3), we get,

⇒ 10/y = 3/5 – 2/4

⇒ 10/y = (12 – 10)/20 = 2/20

⇒ 10/y = 1/10

⇒ y = 100

Now, substitute y = 100 in equation (1)

16/x + 12/100 = 1/5

16/x = 1/5 – 12/100

16/x = 8/100

x = 1600/8 = 200

Hence, Ratio = (1/y)/(1/x) = x/y

Ratio = 200/100 = 2/1 = 2:1

Therefore, the correct option is (A)

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