Question

Separately, Jack and Sristi invested the same amount of money in the stock market. Jack’s invested amount kept getting reduced by 50% every month. Sristi's investment is 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 They observed that if they had withdrawn their respective amounts at the end of the fourth month, the ratio of their amounts would have been the same as the ratio after the sixth month.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?

• A. Rs. 100000
• B. Rs. 120000
• C. Rs. 150000
• D. Rs. 180000
• E. None of the above

Answer 1

The Correct Option is A

Let's denote the initial investment amount by Jack and Sristi as Rs. P. 
1. For Jack, his investment reduces by 50% each month. Thus:
- After 1st month: \( P \times \frac{1}{2} \)
- After 2nd month: \( P \times \left(\frac{1}{2}\right)^2 \)
- After 3rd month: \( P \times \left(\frac{1}{2}\right)^3 \)
- After 4th month: \( P \times \left(\frac{1}{2}\right)^4 \)
- After 5th month: \( P \times \left(\frac{1}{2}\right)^5 \)
- After 6th month: \( P \times \left(\frac{1}{2}\right)^6 \)
2. For Sristi, her investment follows an arithmetic progression (AP) with a common difference of Rs. 15000. Thus:
- After 1st month: \( P - 15000 \)
- After 2nd month: \( P - 2 \times 15000 \)
- After 3rd month: \( P - 3 \times 15000 \)
- After 4th month: \( P - 4 \times 15000 \)
- After 5th month: \( P - 5 \times 15000 \)
- After 6th month: \( P - 6 \times 15000 \)
3. The problem states that the ratio of their remaining amounts after the 4th and 6th months are the same.
Thus:
\[\frac{P \times \left(\frac{1}{2}\right)^4}{P - 4 \times 15000} = \frac{P \times \left(\frac{1}{2}\right)^6}{P - 6 \times 15000}\]
Simplifying, we get:
\[\frac{\left(\frac{1}{2}\right)^4}{P - 60000} = \frac{\left(\frac{1}{2}\right)^6}{P - 90000}\]
\[\frac{16}{P - 60000} = \frac{4}{P - 90000}\]
Cross multiply:
\[16(P - 90000) = 4(P - 60000)\]
Simplifying:
\[16P - 1440000 = 4P - 240000\]
\[12P = 1200000\]
\[P = 100000\]
The amount of money invested by Jack in the stock market was Rs. 100000.