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XAT 2023 — QA & DI Question 16

Simple & Compound InterestEasy

Separately, Jack and Sristi invested the same amount of money in a stock market. Jack’s invested amount kept getting reduced by 50% every month. Sristi’s investment also reduced every month, but in an arithmetic progression with a common difference of Rs. 15000. They both withdrew their respective amounts at the end of the sixth month. They observed that if they had withdrawn their respective amounts at the end of the fourth month, the ratio of their amounts would have been the same as the ratio after the sixth month. What amount of money was invested by Jack in the stock market? 

Answer & solution

  • Rs. 100000

  • B

    Rs. 120000

  • C

    Rs. 150000

  • D

    Rs. 180000

  • E

    None of the above 

Solution

Let their initial amounts be Rs. x

After 4 months:
Jack's investment after 4 months = x × (12)4 = x16
Sristi's investment after 4 months = x - 15000 × 4 = x - 60000

After 6 months:
Jack's investment after 6 months = x × (12)6 = x64
Sristi's investment after 6 months = x - 15000 × 6 = x - 90000

Ratio of their investments after 4 months = Ratio of their investments after 6 months.

⇒ x/16x-60000 = x/64x-90000

⇒ 4(x - 90,000) = x - 60,000
⇒ 3x = 3,00,000
⇒ x = 1,00,000

Hence, option (a).

XAT 2023 QA & DI Q16: Separately, Jack and Sristi invested the same amount of money in a stock market. Jack’s invested amount — Solution | TheCATExam