The total amount payable for completing a piece of work is Rs. 800. C can do it alone is 24 days, while B can do it alone in 8 days. With the help of A, they complete this work in 3 days. What is the sum of money received by A as his share in completing the work?

Correct option is C

Given:

Total amount for a work = ₹800

C can do it in 24 days

B can do it in 8 days

Formula Used:

Let total work be 1.

Then, work done 1 day =$$\frac{1}{Total\ work}$$​​

Solution:

Work done by C in one day =$$\frac{1}{24}$$​​

Work done by A in one day =$$\frac{1}{8}$$​​

Work done by all three working together in one day =$$\frac{1}{3}$$​​

Work done by A in one day =$$\frac{1}{3} - \frac{1}{24} - \frac{1}{8} =\frac{8-1-3}{24} =\frac{4}{24} = \frac{1}{6}$$​​

Ratio of work done by A: B: C = $$\frac{1}{6} : \frac{1}{8} : \frac{1}{24}$$​​

LCM of 6 , 8 and 24 = 24

 $$A: B: C = \frac{1}{6}\times 24 : \frac{1}{8} \times 24: \frac{1}{24} \times 24$$​​

= 4:3:1

So the total sum of raio = 4+3+1 = 8

A’s share =$$\frac{4}{8} \times 800 = ₹400$$​​