Question

A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:

• A. Rs. 650
• B. Rs. 690
• C. Rs. 698
• D. Rs. 700

Hint:

In simple interest problems, the yearly interest is constant. The difference between the amounts for two years directly gives you the interest for one year.

Answer 1

The Correct Option is C

Step 1 (Understanding the difference).
From 3 years to 4 years, the amount increases from Rs. 815 to Rs. 854. Increase \(= 854 - 815 = Rs.\ 39\). This Rs. 39 is the simple interest} for 1 year. Step 2 (Find interest for 3 years).
Interest for 3 years \(= 39 \times 3 = Rs.\ 117\). Step 3 (Find principal).
Amount after 3 years \(= \text{Principal} + \text{Interest for 3 years}\)
\[ 815 = P + 117 \] \[ P = 815 - 117 = Rs.\ 698 \] Step 4 (Check for 4 years).
Interest for 4 years \(= 39 \times 4 = Rs.\ 156\)
Principal + Interest for 4 years \(= 698 + 156 = Rs.\ 854\) — matches exactly. \[ \boxed{698 \ \text{rupees (Option (c)}} \]