Question

sania was given some money by her father on her birthday .she spent all of it in $5$ shops . in each shop she spent one rupee more than half of what she had when she came in . how much did she get from her father

• A. 30
• B. 120
• C. 46
• D. 62

Answer 1

Let money given to sania by his father $= x$

Spent money at 1st shop = $\frac{x}{2}+1=\frac{x+2}{2}$  

Remaining money =$x-\frac{x+2}{2}=\frac{x-2}{2}$

Spent money at 2nd shop = $\frac{x-2}{4}+1=\frac{x+2}{4}$

Remaining money =$\frac{x-2}{2}-\frac{x+2}{4}=\frac{x-6}{4}$

Spent money at 3rd shop  =$\frac{x-6}{8}+1=\frac{x+2}{8}$                                            

Remaining money =$\frac{x-6}{4}-\frac{x+2}{8}=\frac{x-14}{8}$

Spent money at 4th shop = $\frac{x-14}{16}+1=\frac{x+2}{16}$                                            

Remaining money =$\frac{x-14}{8}-\frac{x+2}{16}=\frac{x-30}{16}$

Spent money at 5th shop = $\frac{x-30}{32}+1=\frac{x+2}{32}$                                            

Remaining money$ =0$

Spent money = Given money

$\frac{x+2}{2}+ \frac{x+2}{4}+ \frac{x+2}{8}+ \frac{x+2}{16} +\frac{x+2}{32}=x$

$\Rightarrow \frac{16x+32+8x+16+4x+8+2x+4+x+2}{32}=x$

$ \Rightarrow \frac{31x+62}{32}=x$

$ \Rightarrow \boxed{x=62}$

Hence,Option(D) is the correct choice.