Question

A alone can finish a piece of work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of total wages of Rs.3000. A will get
A. Rs1200
B. Rs1500
C. Rs1800
D. Rs2000

Answer 1

Hint: In this particular type of question we need to find the efficiency of A and B and further calculate the ratio of their efficiencies. Then we need to divide the wages with respect to the ratio of their efficiencies to get the desired answer.

Complete step-by-step answer:
Time taken by A to complete the work = 10days
Thus work done by A in 1 day or his efficiency = $\dfrac{1}{{10}}$
Also, time taken by B to complete the work = 15days
Thus work done by B in 1 day or his efficiency = $\dfrac{1}{{15}}$
Ratio of their efficiencies = $\dfrac{1}{{10}}:\dfrac{1}{{15}} = 3:2$
We know that the ratio of the efficiencies will also be equal to the ratio of the wages.
Therefore finding out the wages of A,
Wages of A =$\dfrac{3}{{3 + 2}} \times total{\text{ }}wages$
$ = \dfrac{3}{5} \times 3000 = Rs1800$
So the wages of A is $Rs1800$
Correct option is ‘C’

Note - In such particular questions, we need to understand the basic concepts of time and work while solving these kinds of problems. Note that if a person's one day's work =$\dfrac{1}{n}$, then then he will complete the work in 'n' days. If the ratio of the number of men required to complete a work is m : n then the ratio of time taken by them will be n : m. Similarly we can calculate wages of B as
Wages of B =$\dfrac{2}{{3 + 2}} \times total{\text{ }}wages$
$ = \dfrac{2}{5} \times 3000 = Rs600$
So the wages of B is $Rs1200$