Word Problems 4

Problem 4: Three persons namely A, B and C can do a certain work individually in 15 days, 6 days and 10 days respectively. If work becomes 3 times then, A, B and C will finish it  together in how many days ?

Solution :

We arrange this data as under;

For A’s case;

15 days equal to the work


15days = Work


1days =\frac{Work}{15}

So, A’s rate of work is

A's Rate = \frac{1}{15}W

where W stands for work


B's Rate = \frac{1}{6}W

C's Rate = \frac{1}{10}W

For knowing capacity of doing work altogether , we take sum of all three A, B and C’s rates;

\Rightarrow (A's rate + B's rate + C's Rate) = \frac{1}{15}W+ \frac{1}{6}W+ \frac{1}{10}W

\Rightarrow (A's rate + B's rate + C's Rate) =( \frac{1}{15}+ \frac{1}{6}+ \frac{1}{10})W

\Rightarrow (A's rate + B's rate + C's Rate) =( \frac{4+10+6}{60})W

\Rightarrow (A's rate + B's rate + C's Rate) =( \frac{20}{60})W

\Rightarrow (A's rate + B's rate + C's Rate) =( \frac{1}{3})W

So, it means A, B, and C together can do work in one day is 1/3 of work

or we can say ;

\Rightarrow (A + B+ C) rate =( \frac{1}{3})W

or we can write;

\Rightarrow (A + B+ C) 1 day's =( \frac{1}{3})W

Taking 3 to left side;

\Rightarrow (A + B+ C) 3days =W

This means A, B and C can finish work in 3 days






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