A person spends \(\frac13\) of the money with him on clothes, \(\frac

1.	A person spends \(\frac13\) of the money with him on clothes, \(\frac15\) of the remaining on food and \(\frac14\) of the remaining on travel. Now he is left with Rs 100. How much did he have with him in the beginning ? (a) Rs 200 (b) Rs 250 (c) Rs 300 (d) Rs 450
Answer» (b) Let the total money with the person be Rs x. Then, money spent on clothes = Rs \(\frac{x}{3}\) Remaining money = Rs \((x-\frac{x}{3}) =\) Rs \(\frac{2x}{3}\) ∴ Money spent on food = \(\frac15\) x Rs \(\frac{2x}{3}\) = Rs \(\frac{2x}{15}\) Now, remaining money = \(\frac{2x}{3}\) - \(\frac{2x}{15}\) = Rs \(\frac{8x}{15}\) ∴ Money spent on travel = \(\frac14\) x Rs \(\frac{8x}{15}\) = Rs \(\frac{2x}{15}\) Given, \(\frac{x}{3}\) + \(\frac{2x}{15}\) + \(\frac{2x}{15}\) + 100 = x ⇒ \(\frac{5x+2x+2x+1500}{15}\) = x ⇒ x = \(\frac{1500}{6}\) = Rs 250

A person spends \(\frac13\) of the money with him on clothes, \(\frac15\) of the remaining on food and \(\frac14\) of the remaining on travel. Now he is left with Rs 100. How much did he have with him in the beginning ? (a) Rs 200 (b) Rs 250 (c) Rs 300 (d) Rs 450

Answer»

(b) Let the total money with the person be Rs x.

Then, money spent on clothes = Rs \(\frac{x}{3}\)

Remaining money = Rs \((x-\frac{x}{3}) =\) Rs \(\frac{2x}{3}\)

∴ Money spent on food = \(\frac15\) x Rs \(\frac{2x}{3}\) = Rs \(\frac{2x}{15}\)

Now, remaining money = \(\frac{2x}{3}\) - \(\frac{2x}{15}\) = Rs \(\frac{8x}{15}\)

∴ Money spent on travel = \(\frac14\) x Rs \(\frac{8x}{15}\) = Rs \(\frac{2x}{15}\)

Given, \(\frac{x}{3}\) + \(\frac{2x}{15}\) + \(\frac{2x}{15}\) + 100 = x

⇒ \(\frac{5x+2x+2x+1500}{15}\) = x

⇒ x = \(\frac{1500}{6}\) = Rs 250