Question

laxman can do a work in 15 days and bharat can do the two- third work done by ram and laxman together in a day. if bharat completes the work in 18 days, how many days will it take ram to complete the work with bharat?​

Answer 1

Given:

Laxman can do a work in 15 days and Bharat can do the two-third work done by ram and Laxman together in a day

Bharat completes the work in 18 days

To find:

How many days will it take Ram to complete the work with Bharat?​

Solution:

Let's assume,

"R" → represents the no. of days Ram can do the work

"L" → represents the no. of days Laxman can do the work

"B" → represents the no. of days Bharat can do the work

So,

In 1 day, Laxman will do = $\frac{1}{L}$ =  $\frac{1}{15}$ of the work

In 1 day, Ram will do = $\frac{1}{R}$ of the work

In 1 day, Bharat will do = $\frac{1}{B}$ =  $\frac{1}{18}$ of the work

Now, according to the question, we can form an equation as,

[Bharat's 1-day work] = $\frac{2}{3}$ × [Work done by Ram & Laxman together in 1-day]

$\implies \frac{1}{B} = \frac{2}{3} \times [\frac{1}{R} + \frac{1}{L} ]$

substituting the values

$\implies \frac{1}{18} = \frac{2}{3} \times [\frac{1}{R} + \frac{1}{15} ]$

$\implies \frac{1}{12} = \frac{1}{R} + \frac{1}{15}$

$\implies \frac{1}{R} = \frac{1}{12} - \frac{1}{15}$

$\implies \frac{1}{R} = \frac{5-4}{60}$

$\implies \bold{\frac{1}{R} = \frac{1}{60}}$

∴ Ram alone can complete the work in → 60 days.

So,

In 1-day, Ram and Bharat together will complete,

= $\frac{1}{R} + \frac{1}{B}$

= $\frac{1}{60} + \frac{1}{18}$

= $\frac{3+ 10}{180}$

= $\bold{\frac{13}{180}}$

∴ The work done by Ram and Bharat together = $\frac{180}{13}$ = $13.846$ ≈ $14\:days\:approx$

Thus, Ram will take approximately 14 days to complete the work with Bharat.

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