A sum of money becomes ₹34,800 in 2 years and ₹42,000 in 5 years at simple interest per annum. Find the rate of interest and the sum of money respectively.

Correct option is C

Given:
Amount after 2 years = ₹34,800
Amount after 5 years = ₹42,000
Time difference = 5 years − 2 years = 3 years
Formula Used:
Simple Interest (SI) = Amount − Principal
SI = $$\frac{P \times R \times T}{100}$$​​
Solution:
Interest for 3 years = ₹42,000 − ₹34,800 = ₹7,200
Let Principal = P and Rate = R%
For 3 years interest:
7200 = $$\frac{P \times R \times 3}{100}$$​ —— (i)
From 2-year amount:
P + $$\frac{P \times R \times 2}{100}$$​ = 34,800 —— (ii)
Multiply to eliminate fraction:
100P + 2PR = 3480000 —— (iii)
From (i):
PR = $$\frac{7200 × 100} 3$$​ = 240000
Substitute in (iii):
100P + 2 × 240000 = 3480000
100P + 480000 = 3480000
100P = 3000000 => P = ₹30,000
Now, R = $$\frac{240000 }{ 30000}$$​ = 8%