# CAT 2020 Quant Question [Slot 1] with Solution 22

Question

A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffees and one extra to the first child, and then the half of the remaining stock along with one extra to the second and continues giving away in this fashion. His total stock exhausts after he takes care of 5 children. How many toffees were there in his stock initially?

Option: 62
Solution:

Given that the person is left with no toffees after distributing them to the fifth student.

Also given that to each student the person gave one more than half the number of toffees at that stage.

For these types of problems, better we go for backward calculation. If the person had not given 1 extra toffee, he would have left with that toffee.

This represents that he had 2 toffees at that stage. In the previous stage i.e in ${4^{{\text{th }}}}$ stage he should have (2 +1)$\times 2$ i.e 6 toffees In the third stage, he should have $(6 + 1) \times 2$ i.e 14 toffees.

In the second stage, he should have $(14 + 1) \times 2$ i.e 30 toffees. In the first stage, he should have $(30 + 1) \times 2$ i.e 62 toffees. Hence he initially had 62 toffees.

CAT 2021 Online Course @ INR 8999 only

## CAT 2020 Quant questions with Solutions

### CAT 2021 Crash Course + Mock Test Series (INR 4999 Only)

• 50 Live Sessions
• 1000+ Practice problems
• 30 Sectional Tests
• 15 CAT Mock Tests (Video Solutions)
• Dedicated Whatsapp group for doubt clearing
• Valid till 31st March 2022
 Bodhee Prep's YouTube channel CAT Prep Whatsapp Group CAT Prep Telegram Group
X
 CAT prep Telegram Group