Exercise : 1


1. Arun borrowed a sum of money from Jayant at the rate of 8% per annum simple interest for the first four years, 10% per annum for the next six years and 12% per annum for the period beyond ten years. If he pays a total of 12,160 as interest only at the end of 15 years, how much money did he borrow?
(a) 8000
(b) 10,000
(c) 12,000
(d) 9,000
(e) None of these
Ans.a

Let the Principal = P

Then \(\frac{P \times 8 \times 4}{100} + \frac{P \times 10 \times 6}{100} + \frac{P \times 12 \times 5}{100}\)

= 12160

⇒ 152P = 12160 × 100

or \(\frac{12160 \times 100}{152} = 8000\)

2. A sum fetched total simple interest of 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?
(a) 8925
(b) 8032.50
(c) 4462.50
(d) 8900
(e) None of these
Ans.a

Let the sums be P.

Now, 45% of P = 4016.25

or, P = 8925

3. At a simple interest 800 becomes 956 in three years. If the interest rate, is increased by 3%, how much would 800 become in three years?
(a) 1020.80
(b) 1004
(c) 1028
(d) Data inadequate
(e) None of these
Ans.c

Rate of interest = \(\frac{956 - 800}{3 \times 800} \times 100 = 6.50 \%\)

\Amount = 800 + \(\frac{800 \times 9.5 \times 3}{100}\)

= 800 + 228 = 1028

4. On 3,000 invested at a simple interest rate 6 p.c.p.a, 900 is obtained as interest in certain years. In order to earn 1,600 as interest on 4,000 in the same number of years, what should be the rate of simple interest?
(a) 7 p.c.p.a.
(b) 8 p.c.p.a.
(c) 9 p.c.p.a.
(d) Data inadequate
(e) None of these
Ans.b

Time = \(\frac{900 \times 100}{3000 \times 6}\) = 5 years

Rate = \(\frac{1600 \times 100}{5 \times 4000}\) = 8%

5. Ashok borrowed some money at the rate of 6% p.a. for the first two years, at the rate of 9% p.a. for the next three years and at the rate of 14% p.a. for the period beyond five years. If he pays a total interest of 11,400/ - at the end of nine years, how much money did he borrow?
(a) 16,060
(b) 14,000
(c) 18,000
(d) 12,000
(e) None of these
Ans.d

We have, SI = \(\frac{p \times r \times t}{100}\)

∴ 11400 = \(\frac{p \times 6 \times 2}{100} + \frac{p \times 9 \times 3}{100} + \frac{p \times 14 \times 4}{100}\)

or,12p + 27p + 56p = 11400 × 100

or, 95p = 11400 × 100

∴ p = 12000

6. A certain amount earns simple interest of 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?
(a) 35
(b) 350
(c) 245
(d) Cannot be determined
(e) None of these
Ans.d

Let p and r be the principal amount and rate of interest respectively.

Then, \(\frac{p \times r \times 7}{100} = 1750\)

or, pr = 25000

Now, SI = \(\frac{p \times \left(r + 2 \right) \times 7}{100} = 1750\)

We have to find the value of

\(\frac{p \times \left(r + 2 \right) \times 7}{100} - \frac{p \times r \times 7}{100}\) = M - 1750

M = SI when the rate of interest is 2% more. When we solve this equation, we find that we have two variables and one equation. Therefore, can’t be determined the correct answer.

7. What will be the difference in simple and compound interest on 2000 after three years at the rate of 10 percent per annum?
(a) 160
(b) 42
(c) 62
(d) 20
(e) None of these
Ans.c

For 3 years:

\(Diff. = \frac{Sum \times \left(rate \right)^{2} \left(300 + rate \right)}{\left(100 \right)^{3}}\)

= \(\frac{2000 \times 10 \times 10 \times 310}{100 \times 100 \times 100}\) = 62

8. Nikhilesh invested certain amount in three different schemes A, B and C with the rate of interest 10 p.c.p.a., 12 p.c.p.a.and 15 p.c.p.a. respectively. If the total interest accrued in one year was 3200 and the amount invested in scheme C was 150% of the amount invested in scheme A and 240% of the amount invested in scheme B, what was the amount invested in scheme B?
(a) 8000
(b) 5000
(c) 6500
(d) Cannot be determined
(e) None of these
Ans.b

Ratio of Nikhilesh’s investments in different schemes

= \(100 : \frac{150 \times 100}{240} : 150 = 8 : 5 : 12\)

Now, according to the question,

\(\frac{8k \times 10}{100} + \frac{5k \times 12}{100} + \frac{12k \times 15}{100}\) = 3200

or, 80k + 60k + 180k = 3200 × 100

or, 320k = 3200 × 100

or, k = 1000

∴ amount invested in scheme B will be = 1000 × 5 = 5000

9. Aniket deposited two parts of a sum of 25000 in different banks at the rates of 15% per annum and 18% per annum respectively. In one year he got 4050 as the total interest. What was the amount deposited at the rate of 18% per annum?
(a) 9000
(b) 18000
(c) 15000
(d) Data inadequate
(e) None of these
Ans.e

Let the amount deposited at the rate of 15% per annum be x.

15% of x + 18% of (25000 – x) = 4050

or, 15% of x + 18% of 25000 – 18% of x = 4050

or, 3% of x = 4500 – 4050 = 450 ⇒ x = 15000

\ Amount deposited at 18% = (25000 – 15000 ) = 10000

10. Mr X invested an amount for 2 years @ 15 p.c.p.a at simple interest. Had the interest been compounded, he would have earned 450/- more as interest. What was the amount invested?
(a) 22000
(b) 24000
(c) 25000
(d) Data inadequate
(e) None of these
Ans.e

\(\frac{30p}{100} + 450 = p + \frac{15}{100} - p\)

⇒ p = 20,000.