XAT 2023 Question Paper | Quantitative Aptitude and Data Interpretation

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Question 21 : 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 They observed that if they had withdrawn their respective amounts at the end of the fourth month, the ratio of their amounts would have been the same as the ratio after the sixth month.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?

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Video Explanation

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Explanatory Answer

	Jack	Sristi
Investment	x	x
Month 1	\( \frac { x } { 2 } \)	x - 15,000
Month 2	\( \frac { x } { 4 } \)	x - 2(15,000)
Month 3	\( \frac { x } { 8 } \)	x - 3(15,000)
Month 4	\( \frac { x } { 16 } \)	x - 4(15,000)
Month 5	\( \frac { x } { 32 } \)	x - 5(15,000)
Month 6	\( \frac { x } { 64 } \)	x - 6(15,000)

They observed that if they had withdrawn their respective amounts at the end of the fourth month, the ratio of their amounts would have been the same as the ratio after the sixth month.
\( \frac { \frac { x } { 16 } } { x - 4 ( 15,000 ) } = \frac { \frac { x } { 64 } } { x - 6 ( 15,000 ) } \)
\( \frac { 4 } { x - 60,000 } = \frac { 1 } { x - 90,000 } \)
\( 4 ( x - 90,000 ) = x - 60,000 \)
\( 3 x = ( 4 ( 90 ) - 60 ) \times 1000 \)
\( 3 x = 3,00,000 \)
\( x = 1,00,000 \)

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The answer is 'Rs. 100000'

Choice A is the correct answer.