1. What annual payment will discharge a debt of Rs. 1620 dues in 5 years at 4% p.a. SI.
Sol:
B = 1620
n = 5
y = 1
r = 4%
∴ B = \(na + \frac{{ra}}{{100y}} \times \frac{{n(n – 1)}}{2}\)
1620 = \(5a + \frac{{4a}}{{100 \times 1}} \times \frac{{5 \times 4}}{2}\)
a = 300 Rs. Answer
Method(2):
∴ installment = 100 unit = 100×3 = 300 Rs. Answer
2. A sum of Rs. 5000 is lent for 4 years at the rate of 5% p.a. at SI. Find the interest.
Sol:
SI = \(\frac{{5000 \times 4 \times 5}}{{100}}\) = 1000 Rs. Answer
3. If the simple interest on Rs. 900 increases by Rs. 30 when the time increases by 2 years. Find the rate percent per annum.
Sol:
Method(1):
\(\frac{{900 \times r \times (t + 2)}}{{100}} – \frac{{900 \times r \times t}}{{100}} = 30\)
\(\frac{{900 \times r \times 2}}{{100}} = 30\)
r = \(\frac{5}{3}\)% Answer
Method(2):
\(\frac{{900}}{{100\% }}\left( {r(t + 2) – rt} \right)\% = 30\)
\(\frac{{900 \times 2r}}{{100}} = 30\)
r = \(\frac{5}{3}\)% Answer
4. A man deposited Rs. 5460 in a bank at 3% p.a. and Rs. 5980 in another bank at 7% p.a. Find the rate of interest for the whole sum.
Sol:
∴ x = \(\frac{{3 \times 21 + 7 \times 23}}{{21 + 23}}\)
= 5.09% Answer
5. The simple interest on a sum of money is \(\frac{9}{{16}}\) of principal, and the number of years is equal to the rate percent per annum. Find rate percent.
Sol:
\(\frac{9}{{16}}P\) = \(\frac{{P \times r \times r}}{{100}}\)
r² = \(\frac{{900}}{{16}}\)
r = \(\frac{{30}}{4}\) = 7.5% Answer
6. A sum was put on SI at a certain rate for 3 years. Had it been put at 5% higher rate it would have fetched Rs. 750 more, find the sum.
Sol:
SI ∝ rt
∴ if r ↑ 5% higher then it would fetch extra 3×5% = 15% interest.
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7. The SI on a sum of money will be Rs. 200 in after 5 year. For the next 7 years principal becomes 6 times, what will be the total interest at the end of 12 years.
Sol:
required SI = \(200 + \frac{{200}}{5} \times 7 \times 6\)
= 1880 Rs. Answer
8. A certain sum is invested for a certain time period. It amounts to Rs. 200 at 5% p.a. But when invested at 10% p.a., it amounts to Rs. 300. Find the time.
Sol:
Make principal same in both the cases
\(\frac{{200}}{{(100 + 5t)\% }} \times 100\% = \frac{{300}}{{(100 + 10t)\% }} \times 100\% \)
300 + 15t = 200 + 20t
5t = 100
t = 20 years Answer
9. If the simple interest on Rs. 1660 be more than SI of 1560 Rs. by Rs. 30 in 5 years. Find the rate percent per annum.
Sol:
\(\frac{{1660}}{{100\% }} \times 5r\% – \frac{{1560}}{{100\% }} \times 5r\% = 30\)
\(\frac{{100}}{{100}} \times 5r = 30\)
r = 6% Answer
10. If the simple interest on Rs. 440 increases by Rs. 55, when the rate percent increases by 5% p.a. Find the time.
Sol:
\(\frac{{100\% }}{{440}} \times 55 = (r + 5)t\% – rt\% \)
\(\frac{{25}}{2}\) = 5t%
t = 2.5 years Answer