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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?

A
56
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B
48
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C
42
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D
38
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Solution

## The correct option is C 42Let 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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