Question

Rita spends 1⁄4 of her pocket money on chocolates, 1⁄8 on pizza. At the end she had Rs 40 left. How much did she have at the beginning?

Answer 1

Answer:

If Rita spends 1/4 of her pocket money on chocolates and 1/8 on pizza and at the end, she had Rs 40 left, then the amount of pocket money she had at the beginning is Rs 64

Step-by-step explanation:

Let X be the total amount of pocket money Rita had at the beginning

Given

Amount of money Rita spends on chocolates = 1/4 th of her pocket money = $\frac{1}{4} *X$

Amount of money she spends on pizza = 1/8 th of her pocket money = $\frac{1}{8}*X$

Amount of money she had at the end = Rs 40

The total amount of pocket money Rita had at the beginning = Amount of money Rita spends on chocolates + Amount of money she spends on pizza + Amount she had at the end

That is, X= $\frac{1}{4}*X$ + $\frac{1}{8}*X$ + 40

$X=\frac{8X+4X}{8*4} + 40$

$X=\frac{12X}{8*4} +40$

$X= \frac{3}{8} X +40\\\\X-\frac{3}{8}X =40$

$\frac{8X-3X}{8}=40$

$5X= 40*8\\\\X= \frac{40*8}{5} \\\\X= 8*8\\\\X=64$

So the amount of pocket money Rita had at the beginning is Rs 64