A sum becomes ₹500 in 5 years and ₹600 in 7 years at a certain rate percent p.a at of simple interest. What is the sum?

A sum becomes ₹500 in 5 years at a certain rate percent p.a at of simple interest.

Here P = principal amount and R = rate of interest.

$$500=P+\frac{P\times\ R\times\ 5}{100}$$

$$500=P+\frac{\ 5PR}{100}$$

$$500=\frac{100P}{100}+\frac{\ 5PR}{100}$$

$$50000=100P+\ 5PR$$

$$600=P+\frac{P\times\ R\times\ 7}{100}$$

$$600=\frac{100P}{100}+\frac{7PR}{100}$$

$$60000=100P+7PR$$    Eq.(ii)

Put Eq.(i) in Eq.(ii).

$$60000=100P+7(10000-20P)$$

60000=100P+70000-140P

140P-100P = 70000-60000

40P = 10000

Sum = P = ₹250