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Question

3 men and 4 boys can do a piece of work in 14 days, while 4 men and 6 boys do the same work in 10 days. How long would it take one man to finish the same work ?

A
40 days
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B
20 days
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C
35 days
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D
70 days
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Solution

The correct option is D 70 days
Let one man's one day's work be x
Let one boy's one day's work be y
According to first condition,
3x+4y=114 .......Equation 1
According to second condition,
4x+6Y=110 .......Equation 2
Multiplying Equation 1 by 4 and Equation 2 by 3,
12x+16y=414 .....Equation 3
12x+18y=310 .....Equation 4
Now solving Equation 3 and 4 simultaneously by substracting Equation 3 by Equation 4,
we get,
2y=414310

2y=4042140

y=1140
Putting the value of y in equation 1, we get,
3x+4140=114

x=170

Hence one man's one day work is 170

one man completes the whole work in 70 days.

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