Question

if 8 men or 17 boys can do a piece of work in 26 days, how many days will ot take for 4 men and 24 boys to a piece of work 50×0.09 times as great?​

Answer 1

Answer:

It takes 62 days for 4 men and 24 boys to complete the given work

Step-by-step explanation:

The proper question is,-"If 8 men or 17 boys can do a piece of work in 26 days, how many days will it take for 4 men and 24 boys to a piece of work  which is 50×0.09 times the initial work ?​

Given that,

8 men or 17 boys can do a piece of work in 26 days.

Let us assume that 1 unit of work needs to be done.

Hence,work done by 8 men or 17 boys in 1 day is $\frac{1}{26}$

=>Work done by 1 man in 1 day is $\frac{1}{26\times8} =\frac{1}{208}$

=>Work done by one boy in 1 day is $\frac{1}{26\times17} =\frac{1}{442}$

Now we are required to find the time taken by 4 men and 24 boys together to complete a work $50\times 0.09=4.5$ times as great as initial work(i.e,4.5 units of work)

Work done by 4 men and 24 boys in 1 day is calculated as shown below

$=\frac{4}{208} +\frac{24}{442}=0.073units$

Hence,to complete 4.5 units of work,the no.of days taken will be

$\frac{4.5}{0.073} =61.64\approx62days$

Hence it takes 62 days for 4 men and 24 boys to complete the given work

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