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Question

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
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B
3 : 1
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C
3 :2
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D
5 : 4
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Solution

The correct option is A 2 : 1
Let 1 man's 1 days' work = x and 1 boy's 1 days' work = y
Then 12 x + 16y = $$\displaystyle \frac {1}{5}.............(i)$$
         13x + 24y =  $$\displaystyle \frac {1}{4}.............(ii)$$
Multiplying (i) by 3 and (ii) by 2 we get 
         36 x + 48y = $$\displaystyle \frac {3}{5}.............(iii)$$
         26x + 48y = $$\displaystyle \frac {1}{2}.............(iv)$$
Subtracting eqn (iv) from eqn (iii) we get $$\displaystyle 10x=\frac{3}{5}-\frac{1}{2}=\frac{6-5}{10}=\frac{1}{10}\Rightarrow x=\frac{1}{10}$$
Putting x = $$\displaystyle \frac{1}{100}$$ in (i) we get $$\displaystyle \frac{12}{100}+16y=\frac{1}{5}\Rightarrow 16y=\frac{1}{5}-\frac{12}{100}=\frac{20-12}{100}=\frac{8}{100}\Rightarrow y=\frac{1}{200}$$
$$\therefore$$ Required ratio = $$\displaystyle x:y=\frac{1}{100}:\frac{1}{200}=2:1$$

Mathematics

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