Paper 1 · Mathematical Reasoning and Aptitude
UGC NET December 2022 (24.02.2023) Shift-II
A man invests some amount of money for some time period. This amount becomes Rs 4500 at the rate of 7 percent simple interest. However, if invested at 5 percent per annum simple interest, the same amount becomes Rs 3500. Find the amount of money and the time period.
ARs 1000, 50 years ✓ Correct
BRs 2000, 50 years
CRs 1000, 30 years
DRs 2000, 30 years
Correct answer: (A) Rs 1000, 50 years — The amount is Rs 1000 and the time is 50 years, so the answer is Rs 1000, 50 years.
Explanation
★The amount is Rs 1000 and the time is 50 years, so the answer is Rs 1000, 50 years.
★Let the principal be x and the time be n years.
★At 7 percent the interest is 4500 minus x, and at 5 percent it is 3500 minus x.
★So 7 times x times n over 100 equals 4500 minus x, and 5 times x times n over 100 equals 3500 minus x.
★Dividing one equation by the other and solving gives x equal to 1000.
★Substituting back gives the time n equal to 50 years.
★So the amount is Rs 1000 and the time is 50 years.
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