Question

Eesha, babu and chitra work in a handicraft factory. Eesha alone takes 10 hours to complete a single product but babu and chitra working together take 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:

Eesha, babu and Chitra together have worked for 40 hours

Step-by-step explanation:

Time taken by Eesha to complete a product = 10 hours

In 10 hours Eesha completes = 1 product

Therefore, in 1 hour, Eesha completes = 1/10 product

Let in 1 hour Babu completes = 1/x product

And in 1 hour Chitra completes = 1/y product

In 1 hour Babu and Chitra both complete = $\frac{1}{x}+\frac{1}{y}$ product

In 4 hour Babu and Chitra complete 1 product

Therefore,

$4(\frac{1}{x}+\frac{1}{y})=1$

or, $\frac{1}{x}+\frac{1}{y}=\frac{1}{4}$   ........... (1)

If all three are working together then in one hour they will complete = $\frac{1}{10}+\frac{1}{x}+\frac{1}{y}$ product

Let in n hours they complete 14 products

Then,

$n(\frac{1}{10}+\frac{1}{x}+\frac{1}{y})=14$

$\implies n(\frac{1}{10}+\frac{1}{4})=14$

$\implies n(\frac{2+5}{20})=14$

$\implies n(\frac{7}{20})=14$

$\implies n=14\times \frac{20}{7}=40$

Thus, they have worked for 40 hours