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Question

A lady went shopping and spent half of what she had on buying hankies and gave a rupee to a begger waiting outside the shop. She spent half of what was left on a lunch and followed that up with a two rupee tip. She spent half of the remaining amount on a book and three rupees on bus fare. When she reached home, she found that she had exactly one rupee left. How much money did she start with?

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Solution

The correct option is **C** 42

Let the amount, a lady has in the begining

= ₹ x

In first case, amount spent =x2

Given to begger = ₹1

∴ Balance = x−(x2+1)=x−(x+22)=2x−x−22 = x−22

Amount spent on lunch =x−22 × 12 = x−24

Given to tip = ₹2

∴ Balance =x−22−(x−24+2)

=x−22−x−24−2

=2(x−2)−(x−2)−2×44

=2x−4−x+2−84

=x−2−84=x−104

Amount spent on purchase of a book

=x−104×2=x−108

Given as bus fare = ₹3

∴ Balance =x−104−(x−108+3)

=x−104−x+108−3=x−108−3

According to the condition :

x−108−3=1

⇒x−108=1+3

⇒x−108=4

⇒x−10=32

⇒x=32+10=42

The lady has ₹42 in the beginning.

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