At a certain rate simple interest per annum, a certain sum amounts to ₹24,000 in 7 years and to ₹32,000 in 12 years. What is the rate of simple interest paid per annum ?

12.5%

Simple interest of ( 12 - 7 ) years = 32000 -  24000 = 8000

Simple interest of 5 years = 8000

Simple interest of 1 year = \(\frac{8000 }{5 }\) = 1600

Simple interest of 7 years = 7 × 1600 = 11200

Initial sum = 24000 - 11200 = 12800

Simple Interest = \(\frac{Principal ×Rate × Time }{100}\)

1600 = \(\frac{12800 ×Rate × 1 }{100}\)

Rate = 12.5%