Simple Interest 1/1

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1. The interest earned by Rs.4800 in 2 years and 3 months at the rate of $8\displaystyle\frac{1}{2}\% $p.a. simple interest is
a. 918
b. 922
c. 925
d. 928

Answer: A

Explanation:
Formula = P × R% × T = $\dfrac{{4800 \times 8\frac{1}{2} \times 2\dfrac{3}{{12}}}}{{100}}$ = $\dfrac{{4800 \times \dfrac{{17}}{2} \times \dfrac{9}{4}}}{{100}}$ = $\dfrac{{4800 \times 17 \times 9}}{{800}}$ = 918

Alternate method:
First we calculate the simple interet for 1 year at $8\displaystyle\frac{1}{2}\% $.
We know that 8.5% (principal) = (10% - 1.5% ) principal
10% (4800) = 480
1% (4800) = 48
0.5% (4800) = 24
Therefore 8.5% (4800) = [10% - (1 + 0.5)%] (4800) = 480 - 48 - 24 = 408
Now 2 years interest = 408 × 2 = 816
3 months interest = 1/4 rd of one year interest = 408/4 = 102
So total interest for 3 years and 4 months = Rs.918

2. What sum of money will amount of Rs. 1768 in 3 years at simple interest if the rates of interest for the three years are $2\displaystyle\frac{1}{4}\% ,3\displaystyle\frac{1}{2}\% ,4\displaystyle\frac{3}{4}\% $respectively
a. Rs.1600
b. Rs.1700
c. Rs.1800
d. Rs.1600

Answer: D

Explanation:
Amount = Principal + Simple interest
As simple interest is independent of each year, we can add all these percentages and calculate directly on the principal.
$ \Rightarrow 2\displaystyle\frac{1}{4}\% + 3\displaystyle\frac{1}{2}\% + 4\displaystyle\frac{3}{4}\% = 10\displaystyle\frac{1}{2}\% $
Given 1768 = P + 10.5% (P) = P + $\displaystyle\frac{{21}}{{200}}$ P
$ \Rightarrow 1768 = \displaystyle\frac{{221}}{{200}}P \Rightarrow P = 1600$

3. Murali deposited a certain sum of money at S.I, which amounts to Rs. 720 after 2 years and to Rs. 1020 after a further period of 5 years. The sum is
a. Rs.500
b. Rs.600
c. Rs.1200
d. Rs.1300

Answer: B

Explanation:
We can observe here that the amount grew upto Rs.1020 after a further period of 5 years. This implies that interest is being added to the principal every year for the next 5 years. So Rs.300 has been added in 5 years. That is for every year the bank must have added Rs.60 to the account. Now for the first two years bank has added Rs.120.
So the money deposited by Murali = Rs.720 - 120 = Rs.600

4. The simple interest on a sum of money will be Rs.600 after 10 years. If the principle is trebled after 5 years, what will be the total interest at the end of the tenth year?
a. Rs.1050
b. Rs.1100
c. Rs.1200
d. Rs.1300

Answer: C

Explanation:
We know that interest is directly proportional to time and principal. If the total interest for 10 years is Rs.600, It is Rs.300 for the first 5 years. Now the principal trebled after 5 years. So we get 3 times more interest for the next 5 years. So instead of Rs.300 we get Rs.900. So total interest = Rs.300 + Rs.900 = Rs.1200

5. An amount becomes 4 times in 7 years when invested under SI at a certain rate. In how many years will the amount become 16 times of the original amount at the same rate ?
a. 25
b. 30
c. 35
d. 40

Answer: C

Explanation:
If we invest Rs.100 in bank it becomes Rs.400 in 7 years. Interest earned on the principal is equal to Rs.300. In other words in 7 years bank gives Rs.300 if we invest Rs.100.
Now if we want to earn 16 times of the investment, then bank has to give 1500 interest for Rs.100. As we know that bank gives Rs.300 for 7 years, We must keep our money in bank for 35 years to get an interest of Rs.1500.
So answer is 35 years.

6. A sum was put at simple interest at a certain rate for 2 years. Had it been put at 4% higher rate, it would have fetched Rs. 400 more. Find the sum.
a. Rs.4500
b. Rs.5000
c. Rs.6000
d. Rs.7500

Answer: B

Explanation:
For two years we got Rs.400 more so for 1 year, we must get Rs.200 extra.
Assume we invested Rs.100 in bank. If bank gives us 4% higher rate it gives Rs.4 extra. To get Rs.200 extra we need to invest 200/4 = 50 times of Rs.100. i.e., Rs.5000

7. Rs. 600 amounts to Rs. 735 in 5 years at a certain rate of Simple interest. If the rate of interest is increased by 2%, what will be the amount then?
a. Rs.795
b. Rs.815
c. Rs.825
d. Rs.850

Answer: A

Explanation:
There is no need of calculating original rate of interest in this case. We can just caluculate the difference generated by the increment of 2% interest rate.
Increase in simple interest = 2% on Rs. 600 for 5 years
= $\frac{{{\rm{600 \times 2 \times 5}}}}{{{\rm{100}}}}$ = 6 × 2 × 5 = Rs. 60
Therefore Amount = Original amount + Extra interest
= Rs. 735 + Rs. 60 = Rs. 795

8. A man lent Rs. 2000 - partly at 5% and the balance at 4%. If he receives Rs. 92 towards annual interest, find the amount lent at 5%.
a. 44
b. 55
c. 60
d. 70

Answer: A

Explanation:
Let the whole amount is invested at 4% p.a. Then, Simple interest = $\displaystyle\frac{{2000 \times 4 \times 1}}{{100}}$ = Rs. 80. This interest is short from actual interest by Rs. 92 - Rs. 80 = Rs. 12
The difference is because the amount is also invested at 5% p.a. Difference in two rates of interest = 5% - 4% = 1% p.a. Here, difference in rate is 1%, and difference in interest = Rs. 12
Therefore, Amount invested at 5% = 12 × $\displaystyle\frac{{100}}{1}$ = Rs. 1200

Alternative Method:
Simple interest on Rs. 2000 at 5% p.a. = $\displaystyle\frac{{{\rm{2000 \times 5 \times 1}}}}{{{\rm{100}}}}$ = Rs. 100
Simple interest on Rs. 2000 at 4% p.a. = $\displaystyle\frac{{{\rm{2000 \times 4 \times 1}}}}{{{\rm{100}}}}$ = Rs. 80
Now, by Alligation Method:

Therefore, Ratio between amounts lent at 5% and 4% = 12 : 8 = 3 : 2
Therefore, Sum lent at 5% = $\displaystyle\frac{{\rm{3}}}{{\rm{5}}}$ × 2000 = Rs. 1200

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