Question

Ravi needs 16 more days to complete a work than raju to complete the same work if both of them work together only 15 days are sufficiently how many days raju alone to complete the same work.

Answer 1

Given:

Ravi needs 16 more days to complete a work than Raju to complete the same work

Both Ravi and Raju can complete the work in 15 days

To find:

No. of days Raju alone will take to complete the same work

Solution:

If "x" days is the no. of days Raju takes to complete the work alone, then "(x + 16)" days is the no. of days that Ravi will take to complete the same work alone.

In 1 day, the amount of work done by Raju = $\frac{1}{x}$

In 1 day, the amount of work done by Ravi = $\frac{1}{x \:+\: 16}$

In 1 day, the amount of work done by both Raju & Ravi together = $[\frac{1}{x}+\frac{1}{x \:+\: 16}]$

But it is given that they together can finish the work in 15 days

∴ $[\frac{1}{x}+\frac{1}{x \:+\: 16}] = \frac{1}{15}$

⇒ $[\frac{x+ x+16}{x(x+16)}] = \frac{1}{15}$

⇒ $[\frac{2x+16}{x^2+16x}] = \frac{1}{15}$

⇒ $15 (2x + 16) = x^2 + 16x$

⇒ $30x + 240 = x^2 + 16x$

⇒ $x^2 + 16x - 30x - 240 = 0$

⇒ $x^2 - 14x - 240 = 0$

⇒ $x^2 - 24x +14x-240 =0$

⇒ $x(x-24) + 10(x - 24) = 0$

⇒ (x - 24)(x + 10) = 0

⇒ x = 24 or -10

no. of days cannot be negative

⇒ x = 24 days

Thus, Raju alone will take 24 days to complete the same work.

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