Question

Sravya bought a watch for Rs. 480. She sold it to Ridhi at a gain of $6\dfrac{1}{4}\% $. Ridhi sold it to Divya at a gain of 10 %. How much did Divya pay for it?

Answer 1

Hint: We have to find the amount Divya paid for the watch. So, first we will find the amount of gain at which Sravya sold it to Ridhi and add it in the original amount of watch. Then, we will find the gain on which Ridhi sold it to Divya and add that in the amount at which Ridhi bought it. And we will get the answer.

Complete step-by-step solution:
Given: The price of the watch when Sravya bought it was 480 Rs.
Sravya sold the watch to Ridhi at the gain of $6\dfrac{1}{4}\% $. First, we will convert $6\dfrac{1}{4}$ in normal fraction.
$ = \dfrac{{25}}{4}\% $
 So, we will find the amount of gain using the percentage formula.
$\dfrac{{25}}{4}\% $of 480 = $\dfrac{{25}}{4} \times \dfrac{{480}}{{100}}$
$ = \dfrac{{25}}{4} \times \dfrac{{48}}{{10}}$
$ = 30Rs.$
 The amount at which Ridhi bought the watch $ = 480 + 30$
$ = 510Rs.$
Now, we will find the amount of gain at which Ridhi sold it to Divya.
Gain = $10\% of510$
$ = 10 \times \dfrac{{510}}{{100}}$
$ = 51Rs.$
Price of watch at which Ridhi sold it $ = 510 + 51$
$ = 561Rs.$
So, Divya paid 561 Rs. for the watch.

Note: A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, ‘%’. The percent value is computed by multiplying the numeric value of the ratio by 100. A percentage is a dimensionless number (pure number); it has no unit of measurement.