Maths question from Panchayat Secretary (VLW) exam, 2025 by JKSSB
Satvir has a sum of 10,000 rupees with him. He invested a part of it at a rate of interest of 10% per annum and other at 8% per annum, both compounded annually. The interest he received after 2 years was 1,926 rupees. In what parts did he divide the sum?
Last updated May 30, 2026
Correct Answer:
Option A —
4,000 and 6,000
To find the correct parts, we can test the given options to see which one results in an interest of exactly 1,926 rupees after 2 years.
When money is compounded annually for 2 years:
At a 10% interest rate, the total interest earned over 2 years is 21% of the invested amount.
At an 8% interest rate, the total interest earned over 2 years is 16.64% of the invested amount.
Let's test Option (C), which splits the money into 7,000 rupees and 3,000 rupees.
Calculating the Interest for Option (C)
First Part: 7,000 rupees invested at 10%
Interest for the first year: 10% of 7,000 = 700 rupees.
New total for the second year: 7,000 + 700 = 7,700 rupees.
Interest for the second year: 10% of 7,700 = 770 rupees.
Total interest from this part: 700 + 770 = 1,470 rupees.
Second Part: 3,000 rupees invested at 8%
Interest for the first year: 8% of 3,000 = 240 rupees.
New total for the second year: 3,000 + 240 = 3,240 rupees.
Interest for the second year: 8% of 3,240 = 259.20 rupees.
Total interest from this part: 240 + 259.20 = 499.20 rupees.
Total Combined Interest:
1,470 + 499.20 = 1,969.20 rupees.
This is a bit too high, so we need to put a little less money into the higher 10% interest rate.
Calculating the Interest for Option (A)
Let's adjust and test Option (A), which splits the money into 6,000 rupees and 4,000 rupees.
First Part: 6,000 rupees invested at 10%
Interest for the first year: 10% of 6,000 = 600 rupees.
New total for the second year: 6,000 + 600 = 6,600 rupees.
Interest for the second year: 10% of 6,600 = 660 rupees.
Total interest from this part: 600 + 660 = 1,260 rupees.
Second Part: 4,000 rupees invested at 8%
Interest for the first year: 8% of 4,000 = 320 rupees.
New total for the second year: 4,000 + 320 = 4,320 rupees.
Interest for the second year: 8% of 4,320 = 345.60 rupees.
Total interest from this part: 320 + 345.60 = 665.60 rupees.
Total Combined Interest:
1,260 + 665.60 = 1,925.60 rupees.
Rounded to the nearest whole rupee, this gives exactly 1,926 rupees.
Conclusion
Satvir divided the money into parts of 6,000 rupees and 4,000 rupees.
Correct Answer: (A) 4,000 and 6,000
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
