Sarah invested amounts in three different schemes M, N, and O at simple interest rates of 10% p.a., 12% p.a., and 15% p.a. respectively. If the total interest accrued in one year was ₹2282 and the amount invested in Scheme O was 180% of the amount invested in Scheme M and 250% of the amount invested in Scheme N, what was the amount invested in Scheme N?
₹3600
Step 1 – express principals in terms of M. Let amount in M = ₹m. Then:
\(O = 1.8m \quad \text{(O is 180\% of M)}\)
\(O = 2.5N \implies N = \dfrac{O}{2.5} = \dfrac{1.8m}{2.5} = 0.72m\)
Step 2 – set up the interest equation (1 year, simple interest):
\(\dfrac{m \times 10}{100} + \dfrac{0.72m \times 12}{100} + \dfrac{1.8m \times 15}{100} = 2282\)
\(0.10m + 0.0864m + 0.27m = 2282\)
\(0.4564m = 2282 \implies m = 5000\)
Step 3 – compute N:
\(N = 0.72 \times 5000 = 3600\)
Hence, the amount invested in Scheme N is ₹3,600.
Similar Questions
Aman needed ₹30,000 for a start-up and split the sum between two private lenders under simple-interest terms:
Lender A charges 9% p.a. (simple interest)
Lender B charges 6% p.a. (simple interest)
Aman kept both loans exactly 4 years and then made a single lump-sum payment that settled only the accumulated interest, which came to ₹9,600. After preparing his books of account, Aman discovered that if he had interchanged the principal amounts taken from the two lenders, his four-year interest outgo would have been ₹1,200 less than what he actually paid. How much of the original ₹30,000 did Aman borrow at 9% p.a. from Lender A?
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Important Questions from Simple Interest
- How long will it take for ₹1,500 to become ₹2,040 at a rate of 8% per annum simple interest?
- Find the simple interest (in ₹) if a sum of ₹400 is borrowed for 5.5 years at 12% per annum rate of interest.
- Find the simple interest (in ₹) if a sum of ₹400 is borrowed for 4.5 years at 8% per annum rate of interest.
Find the simple interest (in ₹) if a sum of ₹400 is borrowed for 5.5 years at 4% per annum rate of interest.
- Find the simple interest (in ₹) on ₹1,200 at an interest rate of 3% per month for 11 months.
