BANK & INSURANCE (SIMPLE AND COMPOUND INTEREST) PART 2

Total Questions: 60

21. A invested Rs. 25000 on simple interest in two parts one at 15% and other at 20% for 2 years. The difference between the interests earned is Rs. 3000. Find the ratio of two parts of investment.

Correct Answer: (d) 3 : 2  
Solution:

Let P = principal, R = rate of interest and N = time

Simple Interest = (P × N × R)/100

According to the question,
Let the two parts of investments be Rs. M and Rs. N respectively.

⇒ M + N = 25000 ……(i)

According to the question,
Difference between the interests earned is Rs. 3000

⇒ (M × 20 × 2)/100 − (N × 15 × 2)/100 = 3000
⇒ 20M − 15N = 1,50,000
⇒ 4M − 3N = 30000 ……(ii)

Solving equation (i) and (ii)
⇒ M = Rs. 15000
⇒ N = Rs. 10000

∴ Required ratio = 15000 : 10000 = 3 : 2

22. A borrowed certain amount of money at the rate interest 25% per annum for 18 months. After 18 months, he has to pay a total amount of Rs. 82500. Find the interest he paid after 18 months.

Correct Answer: (e) Rs. 22500
Solution:

Simple Interest = (P × N × R)/100
P = principal, R = rate of interest and N = time

Here,
Rate of interest = 25% and amount = Rs. 82500 and time = 18 months

Let the principal be P
⇒ Amount = P + simple interest
⇒ 82500 = P + (P × N × R)/100
⇒ 82500 = P + 3P/8
⇒ 82500 × 8 = 11P
⇒ P = Rs. 60000

∴ Simple Interest = 82500 − 60000 = Rs. 22500

23. Prashant borrowed Rs. 20000 at 5% p.a. compound interest for 2 years from Yash. After that, he invests it in a bank which offers 8% p.a. simple interest for 2 years. Find the profit earned by Prashant.

Correct Answer: (c) Rs. 1150   
Solution:

Amount to be paid to Yash = P (1 + R/100)ⁿ

= 20000(1 + 5/100)²
= 20000 × (441/400)
= Rs. 22,050

Amount received from bank = P(1 + RT/100)
= 20000(1 + 8 × 2/100)
= Rs. 23,200

∴ Overall profit = 23,200 − 22,050
= Rs. 1,150

24. A merchant had Rs. 10000 to invest. He invested part of the amount in Bank A at 10% simple interest. He invested the remaining amount in Bank B at 10% compound interest. After three years, the amount in Bank B was 50% more than the amount in bank A. How much amount did he invest in Bank A?

Correct Answer:   (d) Rs. 4056.69
Solution:

The amount after 3 years in Bank A = 1.3 (10000 − x)
= 13000 − 1.3x

The amount after 3 years in Bank B = 1.13x = 1.331x

⇒ 1.331x/(13000 − 1.3x) = (3/2)

⇒ 2.662x = 39000 − 3.9x
⇒ 2.662x + 3.9x = 39000
⇒ 6.562x = 39000
⇒ x = 39000/6.562 = Rs. 5943.31

∴ The amount invested in Bank A = 10000 − 5943.31
= Rs. 4056.69

25. Keya borrows Rs 25000 from shree at 10% compound rate of interest. At the end of each year she pays Rs 8000 back to shree. At the end of year 3 how much amount would be left for to pay?

Correct Answer: (e) Rs. 6795
Solution:

Amount to be paid at end of year 1 = 25000 × (1 + 0.10)
⇒ Amount = 27500

⇒ P for Year 2 = 27500 − 8000
⇒ P = 19500

⇒ A for year 2 = 19500 × 1.10
⇒ A = 21450

⇒ P for year 3 = 21450 − 8000
⇒ P = 13450

⇒ A for year 3 = 13450 × 1.10
⇒ A = 14795

⇒ P for year 4 = 14795 − 8000
⇒ P for year 4 = 6795

∴ at end of year 3 keya will have to pay Rs 6795 to shree

26. The interest earned on investing Rs. ‘Y’ for 4 years at simple interest of 15% p.a. is Rs. 160 more than the interest earned on investing Rs. (Y - 500) for 4 years at simple interest of 16% p.a. Find the value of ‘Y’.

Correct Answer: (d) 4000  
Solution:

Simple interest earned on investing Rs. ‘Y’ = (Y × 4 × 15 ÷ 100) = Rs. 0.6Y

Simple interest earned on investing Rs. (Y − 500) = (Y − 500) × 4 × 16 ÷ 100 = Rs. 0.64Y − 320

According to the question,
0.6Y = 0.64Y − 320 + 160
Or, 0.04Y = 160

So, Y = 160 ÷ 0.04 = 4000

Hence, option d.

27. A man invested a total of Rs. 36,000 in two different schemes for 4 years each, both at simple interest. Rate of interest for given two schemes are 15% p.a. and 24% p.a. If total interest earned by the man is Rs. 28,800, then find the sum invested by him at simple interest of 24% p.a.

Correct Answer: (e) Rs. 20,000
Solution:

Let the sum invested at simple interest of 24% p.a. be Rs. ‘x’.
And, sum invested at simple interest of 15% p.a. be Rs. ‘y’

Effective rate of interest = [(28800/36000) × 100] + 4 = 20%

Using allegation we have;

15% 24%
\ /
20%
/ \
24 − 20 = 4 20 − 15 = 5

Or, x:y = 5:4

Sum invested at simple interest of 24% p.a. = 36000 × (5/9) = Rs. 20,000

Hence, option e.

28. When Rs. ‘P’ is invested at simple interest of ‘R%’ p.a. for 5 years it becomes 2.1 times of itself. If Rs. (P - 250) is invested at simple interest of (R + 26)% p.a. it gives an interest of Rs. 4,896 at the end of 4 years, then find the value of ‘P’.

Correct Answer: (b) 2800  
Solution:

ATQ
{(P × R × 5)/100} = (2.1P − P)
Or, (P × R × 5)/100 = 1.1P

Or, R = (100/5) × 1.1
Or, R = 22

Therefore, R + 2 = 22 + 26 = 48

Now,
{(P − 250) × 48 × 4}/100 = 4896

Or, 1.92 × (P − 250) = 4896

Or, P − 250 = (4896/1.92) = 2550

Or, P = 2550 + 250

Or, P = 2800

Hence, option b

29. Rs. ‘100Y’ when invested for 4 years at simple interest of 13% p.a., yields an interest of Rs. 2340. If Rs. 120Y is invested for 2 years at compound interest (compounded annually) of 10% p.a., then find the amount received.

Correct Answer: (b) Rs. 6534  
Solution:

According to the question,
(100Y × 4 × 13) ÷ 100 = 52Y = 2340

So, Y = 2340 ÷ 52 = 45

And so, sum invested at compound interest = 120Y = 45 × 120 = Rs. 5400

So, required amount received = 5400 × (1 + (10/100))² = 5400 × 1.21 = Rs. 6534

Hence, option b.

30. A sum amounts to Rs. 18,360 when invested for 3 years at simple interest of 12% p.a. in scheme ‘A’. If a sum equal to 80% of that invested in scheme ‘A’, is invested for 2 years at compound interest of 10% p.a., compounded annually, then find the interest received.

Correct Answer: (d) Rs. 2,268  
Solution:

Let the sum invested in scheme ‘A’ = Rs. ‘100y’

Then, 100y × 3 × 12 ÷ 100 + 100y = 18360

Or, 18360 ÷ 136 = 135

So, 80% of sum invested in scheme ‘A’ = 13500 × 0.8 = Rs. 10800

So, compound interest received = 10800 × (1 + (10/100))² − 10800

= 13068 − 10800 = Rs. 2,268

Hence, option d.