Question

The compound interest calculated at a certain rate on a certain sum of money, x for 2nd year and 3rd year is Rs. 770 and Rs. 847, respectively. Find the sum of money x (in Rs.).

• A. 6,000
• B. 6,700
• C. 6,300
• D. 7,000

Answer 1

Answer:

D. 7,000

Solution: Given: Principal amount = x Interest for 2nd year = Rs. 770 Interest for 3rd year = Rs. 847 Concept used: For 1st year interest = (P × R × T)/100 For 2nd year interest, ⇒ ((P + 1st year interest) × R × T) /100 Calculation: Let, Rate of interest = R Difference between the CI of two successive years = 847 - 770 = Rs. 77 So, 77 is the one-year interest on Rs. 770. ⇒ (770 × R × 1)/100 = 77 ⇒ 770 × R = 77 × 100 ⇒ R = 7700/770 = 10 Interest on x for 1st year = (x × 10 × 1)/100 = x/10 = 0.1x Principal amount for 2nd year = (x + 0.1x) = 1.1x Interest on 1.1x for 2nd year = (1.1x × 10 × 1)/100 = 0.11x Now, 0.11x = Rs. 770 ⇒ x = 770/0.11 = 770 × 100/11 = Rs. 7000 ∴ The sum of the money is Rs. 7000.