INTRODUCTION:
Simple Interest: The interest is calculated on the principal, that’s why the interest is constant through out each & every year.
Generally, the problems on S.I & C.I are based on the calculation of percentage i.e. on the out of 100. So if we calculate the S.I & C.I. on a sum of 100 @ any % it is easy to get. Then we can calculate the S.I. & C.I. on the given sum
QUESTION 1:
Find the simple interest on Rs.5000 @ 10% p.a. for 5 years.
Solution:
If the sum is Rs100, then @ 10% p.a. in 1 year the S.I is Rs.10.
In 5 years, on a sum of Rs100 the S.I. is Rs50.
So in 5 years, on a sum of Rs5000 the S.I. is Rs2500.
QUESTION 2:
If a sum of money amounts to Rs13000 @ 6% p.a. in 5 years, find the sum.
Solution:
If the sum is Rs100, then @ 6% pa S.I. in 5 years is Rs30.
The amount is Rs130, when the sum is Rs100.
So the amount is Rs13000, when the sum is Rs10000.
QUESTION 3:
If a sum of money doubles it self in 8years, then it will become treble it self in how many years?
Solution:
If the sum is Rs100 & it becomes Rs200 in which the interest is Rs100 in 8 year’s.
So if the sum Rs100 becomes Rs300 in which the interest is Rs200 i.e. in 16 years.
QUESTION 4: If a sum of money becomes trebles it self in 25 years, find the %p.a.
Solution:
If Rs100 trebles, it becomes Rs300 in which the interest is Rs200 in 25 years.
In 25 years the interest is Rs200.
So in 1 year the interest is Rs8 which is @ 8% p.a. on Rs100.
QUESTION 5:
If a sum of money becomes double @ 12.5% p.a. at S.I., find the time period.
Solution:
On a sum of Rs100, the interest is Rs12.50 in 1 year.
When Rs100 becomes Rs200, the interest is Rs100 i.e. in 8 years.
QUESTION 6:
If the simple interest on Rs2000 increases by Rs240, when the time increases by 4 years. Find the rate percent per annum.
Solution:
In 4 years the interest is more by Rs240.
So in 1 year the interest is more by Rs60 which is 3% p.a.
QUESTION 7:
The simple interest on a sum of money is 1/9 of the principal, and the number of years is equal to the rate percent per annum. Find the rate percent.
Solution:
If the sum is RS 100, then the S.I is Rs100/9.
In this case the time period is equal to the rate percent. So at R*R % the interest is Rs100/9.
So R%= 10/3 i.e. 3 1/3 % p.a.
QUESTION 8: If the simple interest on Rs1200 be more than the interest on Rs1000 by Rs30 in 3 years, find the rate percent per annum.
Solution:
If the rate of interest is 1% p.a. then on these two sums of Rs1200 & Rs1000, in 3 years is Rs6.
When the difference is Rs6, the rate of interest is 1%.
So when the difference is Rs30, the rate of interest is 5%.
QUESTION 9:
If simple interest on Rs5000 increases by Rs200, when the rate % increases by 2% per annum. Find the time period.
Solution:
If the rate % increases by 2% on Rs5000, then in 1 year the interest increases by Rs100 in 1 year.
The interest increases by Rs100, the time period is 1 year.
So when the interest increases by Rs200, the time period is 2 years.
QUESTION 10: A sum was put at S.I. at a certain rate for 2 years. Had it been put at 3% higher rate, it would have fetched Rs150 more. Find the sum.
Sol: If the sum is Rs100 & the rate of interest is 3% higher, then in 2 years the interest is Rs6 more.
When the interest is Rs6 more, the sum is Rs100.
So, when the interest is Rs150 more, the sum is Rs2500.
QUESTION 11: A certain sum of money amounts to Rs1125 in 5 years and to Rs1200 in 8 years. Find the sum and the rate of interest.
Solution:
In 3 years more years, the interest is Rs75.
So in 1 year, the interest is Rs25 & in 5 years the interest is Rs125.
Sum +5 years interest= Rs1125. So the sum is Rs1000.
And the rate of interest is 25/1000*100 i.e.2.5% p.a.
QUESTION 12:
Rakish deposited two parts of a sum of Rs25000 in two different banks @15%p.a. and 18% p.a. respectively. In 2 years he got Rs8100 as the total interest. What was the amount deposited at the rate of 18% p.a.?
Solution:
By applying the alligation method we can find the proportion between the two different sums.
Total interest of Rs8100 on a sum of Rs25000 in 2 years is @ 16.2% p.a.
Rate of interest on Sum:1 Rate of interest on sum:2
15% 18%
16.2%
1.8 % 1.2%
So the proportion between the two sums is 3:2
Total part of the sum i.e. (3+2) parts is Rs25000.
So the deposited at 18% p.a. which is 2 parts i.e. Rs10000.
QUESTION 13:
A man invests an amount of Rs15, 860 in the names of his three sons A,B and C in such a way that they receive the same amount after 2,3 and 4 years respectively. If the rate of simple interest is 5% then find the ratio in which the amount was invested for A,B and C ?
Solution:
After the three different years, their amounts are such as 110%, 115% and 120% and these parts of A, B and C respectively are equal.
In terms of part i.e. 22 parts of A=23 parts of B=24 parts of C (D)
So the ratio among their amount is such as 23*24: 24*22:22*23.
QUESTION 14: A person lent a certain sum of money at 4% S.I. , and in 8 years the interest amounted to Rs340 less than the sum lent. Find the sum lent.
QUESTION 15: The S.I on Rs1250 will be less than the interest on Rs1400 at3% S.I by Rs45.Find the time.
QUESTION 16: Two equal sums are deposited in two banks each at 15% for 3.5 years and 5 years respectively. If the difference between their interests is Rs144, find each sum
QUESTION 17: The difference between the interests received from two different banks on Rs600 for 6 years is Rs72. Find the difference between their rates.
QUESTION 18: A sum of money lent out at S.I amounts to Rs720 in 2 years and to Rs1020 in 7 years. Find the rate percent per annum.
QUESTION 19: Some amount out of Rs9000 was lent at8% per annum and the remaining at 65 per annum. If the total interest from both the fractions in 7 years was Rs3900, find the sum lent at two different rates.
QUESTION 20: What annual payment will discharge a debt of Rs8480 due in 4 years hence at 4% per annum?
QUESTION 21: Out of a certain sum, 1/3rd is invested at 3%, 1/6th at 6% and the rest at 8%. If the S.I for 2 years from all these investments amounts to Rs600, find the original sum.
QUESTION 22: The S.I on certain sum Rs900 is Rs100, and the number of years is equal to the rate percent per annum. Find the rate percent.
QUESTION 23: A certain sum of money is borrowed by a person at 5% S.I for 5 years. If he has to pay Rs100 as interest, find the total amount he has to pay.
QUESTION 24: A lent Rs600 to B for 2 years, and Rs150 to C for 4 years and received altogether from both Rs90 as interest. Find the rate of S.I.
QUESTION 25: Rs3000 invested at a S.I rate 6% per annum; Rs900 is obtained as interest in certain years. In order to earnRs1600 as interest on Rs4000 in the same number of years, what should be the rate of S.I?
QUESTION 26: If the rate of interest rises from 6 ½ to 8%, a man’s income increases by Rs4050. Find the sum.
QUESTION 27: If Rs5600 amount to Rs6678 in 3 ½ years, what will Rs9400 amount to in 5 ¼ years, at the same rate percent per annum S.I?
QUESTION 28: The S.I. on a certain sum of money will be Rs600 after 10 years. If the principal is trebled after 5 years, the total interest at the end of 10 years will be:
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