CAT 1993 — DILR Question 22
Use the following information:
Swetha, Swarna, Sneha and Soumya are four sisters who have an agreement that they share all snacks equally among themselves. One day, uncle Prem gave a box of cookies to Swetha. Since the other sisters were not around, Swetha divided the cookies into four parts, ate her share and put the rest into the box. As she was closing the box, Swarna came in, She took all the cookies from the box and divided them into four equal parts. Swetha and Swarna ate one part each and put the rest into the box. Just then Sneha walked in. She took all the cookies from the box, divided them into four equal parts. The three of them ate their respective shares and put the rest into the box. Later, when Soumya came, she divided all the cookies into four equal parts and all the four sisters ate their respective shares. In total, Soumya ate 3 cookies.
How many cookies did uncle Prem give to Swetha?
Answer & solution
128
- B
156
- C
256
- D
192
Since Soumya was the last one to eat the cookies and she ate 3 cookies, the total number of cookies left when she entered the room = (3 × 4) = 12. This should be Soumya’s share that was left in the box uneaten. Hence, just before Soumya entered, Swetha, Sneha and Swarna would have eaten their share of 12 cookies each. Total number of cookies left when Sneha entered = (12 × 4) = 48. This in turn should have been the combined share of Sneha and Soumya (24 × 2) that was left in the box uneaten. So just before Sneha entered, Swetha and Swarna should have eaten 24 cookies each. In other, words number of cookies left, just before Swarna entered = (24 × 4) = 96. Now this should have been the combined share of Swarna, Sneha and Soumya (3 × 32) that was kept in the box by Swetha . So just before Swarna entered, Swetha must have eaten her share of 32 cookies. Hence, total number of cookies given by Prem uncle = (32 × 4) = 128.
The situation is also shown in the following table:
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Prem uncle gave 128 cookies to Swetha.