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 They observed that if they had withdrawn their respective amounts at the end of the fourth month, the ratio of their amounts would have been the same as the ratio after the sixth month.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

Let the amount invested by Jack and Sristi be $$'x'$$.

Jack's amount after four months will become $$\frac{x}{2^4}$$ and after six months it will become $$\frac{x}{2^6}$$.

Sristi's amount after four months will become $$x-\left(4\times\ 15000\right)$$ and after six months it will become $$x-\left(6\times\ 15000\right)$$

From the given information,

$$\ \frac{\ \ \frac{\ x}{2^4}}{x-\left(4\times\ 15000\right)}=\ \frac{\ \ \frac{\ x}{2^6}}{x-\left(6\times\ 15000\right)}$$

$$\ \ \left(\ x-\left(4\times\ 15000\right)\right)=\ 2^2\times\ \left(x-\left(6\times\ 15000\right)\right)$$

$$3x\ =\ 300000$$

$$x\ =\ 100000$$.

The amount invested by Jack and Sristi is 100000.

Option 'A' is correct.