Multiple choice

A person took Rs. 2,50,000 to buy a house, with the condition to pay 12% interest annually. This amount was to be repaid in a period of 18 years. After a certain number of years, the interest rate was reduced to 7.5%. By the end of the agreed period, the person paid a total of Rs. 4,50,000 as interest. For how many years did the person pay at the reduced interest rate?

  1. 6 years

  2. 8 years

  3. 10 years

  4. 12 years

  5. 14 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let x be the years at 12% and y be the years at 7.5%. Total time x+y = 18. Interest = 250000 * 0.12 * x + 250000 * 0.075 * y = 450000. Dividing by 250000 gives 0.12x + 0.075y = 1.8. Substituting x = 18-y: 0.12(18-y) + 0.075y = 1.8, 2.16 - 0.12y + 0.075y = 1.8, 0.36 = 0.045y, so y = 8.

AI explanation

Let x be the number of years the person paid at the original 12 percent interest rate, meaning the reduced 7.5 percent rate was paid for 18 minus x years. The total simple interest paid is 250000 times 12 percent times x plus 250000 times 7.5 percent times the quantity 18 minus x close quantity, which equals 450000. This simplifies to 30000x plus 337500 minus 18750x equals 450000, so 11250x equals 112500, resulting in x equals 10. The person paid the reduced interest rate for 18 minus 10, which is 8 years.

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