Question

A work is done by three person a, b and

c. A alone takes 10 hours to complete a single product but b and c working together takes 4 hours, for the completion of the same product.If all of them worked together and completed 14 products, then how many hours have they worked?

Answer 1

Answer:

A, B and C have worked together for 42 hours

Step-by-step explanation:

A alone can complete a simple product in 10 hours

Work done by A in 1 hour $=\frac{1}{10}$

(B + C) together can complete a single product in 4 hours

Work done by (B +C) in 1 hour $=\frac{1}{4}$

Total work to complete simple product is LCM of 4 and 10 $=20\hspace{0.1cm}parts$

A's 1 hour work $=\frac{20}{10} = 2\hspace{0.1cm}parts$

(B + C)'s 1 hour work $=\frac{20}{4} = 5\hspace{0.1cm}parts$

(A + B + C)'s 1 hour work $=2 + 5=7\hspace{0.1cm}parts$

7 parts completed by A, B and C together in 1 hour

20 parts completed by A, B and C together in $\frac{20}{7} = 3\hspace{0.1cm}hours\hspace{0.1cm}approximately$

Thus, time taken to complete 1 product is 3 hours

Time taken to complete 14 products is $(3 \times 14) = 42\hspace{0.1cm}hours$

Hence, A, B and C have worked together for 42 hours