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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


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Solution

Step 1: Let us assume

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

One day work of a boy =1x

and one day work of a man =1y

One day work of 16 boys =16x

and one day work of 12 men =12y

Step 2: Making the equation on the given data

Given that,

One day work of 12 men and 16 boys =15

16x+12y=15...1

Similarly,

One day work of 13 men and 24 boys =14

24x+13y=14...2

Step 3: Multiplying by 3 to equation 1 and 2 to equation 2

48x+36y=35...3

48x+26y=24...4

Subtract equation 4 from equation 3 we get,

10y=35-24

10y=12-1020

10y=110

y=100

Now, substitute y=100 in equation 1

16x+12100=15

16x=15-12100

16x=8100

x=16008

x=200

Required Ratio =1y1x

=xy

=200100

=21

Hence, the required ratio =2:1.


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