SIMPLE AND AND COMPOUND
7 1.
INTEREST
Z L B A A N L I O U A T D N E
Find the simple interest on Rs 8600 from 18th October, 2006 to 13th March, 2007 at 8% per annum. Also, find the amount.
Ans. Period
18th Oct. 2006 to 13th March 2007
= (13 + 30 + 31 + 31 + 28 + 13) days = 146 days
Now,, Simple interest = Now
146
=
365
2 5
years
P×R×T
= Rs
©
=
100 8600 × 8 × 2
100 × 5 = Rs 275.20
R E T N I
=
Rs
1376 5
Hence, amount = P + S. I. = Rs 8600 + Rs 275.20 = Rs 8875.20 2.
Ashish lent Rs 10500 to Sunidhi at 7% per annum simple interest. After 5 years, Sunidhi discharged the debt by giving a watch and Rs 13000 in cash. What is the value of the watch ?
Ans. P
= 10500, R = 7% p.a., T = 5 years
Now,
S.I. = S . I. =
∴
P×R×T 100
10500 × 7 × 5 100
= Rs 3675
Amount = P + S. I. = Rs 10500 + Rs 3675 = Rs 14175 Amount given in cash = Rs13000 Thus, balance to be paid = Rs 14175 – 13000 = Rs 1175 Hence, value of watch = Rs 1175
Math Class VIII
1
Question Bank
3.
In how much time will Rs 25,600 amount to Rs 35,664, when money 1 is worth 9 % per annum simple interest ? 4 Ans. A = Rs 35664, P = Rs 25600 Thus, simple interest = A – P = Rs (35,664 – 25,600) = Rs 10,064 R
=
Now, T =
9
1 4
37
Z L B A A N L I O U A T D N E =
4
% p.a.
S.I. × 100
=
10064 ×100 × 4
years
=
1 years = 4 years 4 4
17
P× R 25600 × 37 = 4 years 3 months 4. What sum of money will yield Rs 170.10 as simple interest in 2 years 3 month at 6% per annum ? Ans. Here, I = Rs 170.10, T = 2 years 3 months 3
1 9 2 years = years, R = 6% 12 4 4 I × 100 170.10 × 100 170.10 × 100 × 4 P = Now, = Rs = Rs 9 R ×T 6×9 6× 4 34020 17010 × 2 17010 × 4 = Rs 1260 = Rs = Rs = Rs 27 3× 9 6×9 5. Find the rate of interest when Rs 800 fetches Rs 130 as simple interest in 2 years 6 months. Ans. Here, P = Rs 800, I = Rs 130 =
2
©
years
=
R E T N I
T = 2 years 6 months = 2
6
1 5 2 years = years 2 2
years 12 I × 100 130 × 100 Now, R = % p.a. = 5 P ×T 800 × 2 130 × 100 × 2 130 × 2 130 % p.a. = %= % p.a. = 800 × 5 40 20 13 Thus, rate of interest = % p.a. 2 2 Math Class VIII Question Bank =
6.
Find the time when simple interest on Rs 3.3 lakhs at 6.5% per annum is Rs 75075. Ans. Here, P = 3.3 lakhs = Rs 3.3 ×100000 = Rs 330000 R = 6.5% per annum I = Rs 75075
Z L B A A N L I O U A T D N E
Now, Period (T) =
I × 100 P×R
=
75075 × 100
330000 × 6.5
75075 × 100 × 10
years
75075
years years 330 × 65 330000 × 65 1155 7 1 years = years = 3 years = 330 2 2 7. A man borrowed Rs 1500 on 1st April and returned Rs 1572 on 13th June of same year. Find the rate of interest charged. Ans. Here, P = Rs 1500, A = Rs 1572 T = (29 + 31 + 13) days = 73 days =
©
=
R E T N I =
=
73
365
1 5
years
years
I = A – P = Rs 1572 – Rs 1500 = Rs 72 I × 100
72 × 100 % p.a. = Now, R= 1 P ×T 1500 × 5 72 × 100 72 × 1 % p.a. = = p.a. = 24% p.a. 300 × 1 3 8. At what rate per cent of simple interest will a sum of money double itself in 12 years ? Ans. Let Principal (P) = Rs 100 Amount (A) = Rs 100 × 2 = Rs 200 ∴ Simple Interest (S.I.) = A – P = Rs 200 – Rs 100 = Rs 100 Math Class VIII
3
Question Bank
Period (T) = 12 years Now, R
=
I × 100 P×T
Thus, Rate (R) 9.
=
100 × 100
=
100 × 12
25
=
3
1 8 % p.a. 3
Z L B A A N L I O U A T D N E
Simple interest on a certain sum is
9
of the sum. Find the rate
16 percent and the time if both are numerically equal. Ans. Let sum (P) = Rs 100 9 225 ∴ S.I. = × Rs 100 = Rs 16 4 Also, let Rate (R) = x% p.a. Time (T) = x years 225 100 × × x RT S.I. = = ⇒ 4 100 100
⇒ ∴
x
©
2
=
15 = 4 2
225
2
R E T N I x
=
15 2
=
7
1
2
1 15 7 = p.a. and period years years = % =7 2 2 2 10. What sum will yield Rs 406 as simple interest in 1 year 2 months 1 6 % per annum ? at 4 1 25 % p.a. Ans. Here, S.I. = Rs 406, Rate (R) = 6 % = 4 4 1 7 Period (T) = 1 year 2 months = 1 = years 6 6 I × 100 Now, principal (P) = R×T
Hence, rate
Thus, principal
Math Class VIII
1
=
406 × 100 × 4 × 6 25 × 7
4
= Rs 58 × 96 = Rs 5568.
Question Bank
11.
Manoj lent Rs 7200 to Arjun and a certain sum to Varun at the same time at 10% per annum simple interest. After 3 years, Manoj receives Rs 4092 as interest from two together. Find the sum lent to Varun. Ans.Case I: Principal for Arjun = Rs 7200 R = 10%
Z L B A A N L I O U A T D N E
T = 3 years I=
P ×R ×T
=
100
7200 × 10 × 3 100
Rs
= Rs 72 × 10 × 3 = Rs 2160
Case II:
Let principal for Varun be Rs x
R = 10%
T = 3 years I=
P ×R ×T
= Rs
x × 10 × 3
100 100 Total interest from two together
©
R E T N I
= Rs 2160 +
⇒ 4092 = 2160 + ⇒ 1932 =
3 x
3
10
=
Rs
3 x
10
3 x
10
⇒
4092 = 2160 +
⇒
x
10 ⇒ x = 644 × 10 = 6440 Hence, the sum lent to Varun = Rs 6440.
=
1932 ×
3 x 10
10 3
1 The simple interest on a certain sum of money for 2 years at 2 11% per annum is Rs 1590 more than the simple interest on the 1 same sum for 1 years at 9.5% per annum. Find the sum. 2 Ans. Let the sum of money be Rs x 1 Simple interest on Rs x at 11% p.a. for 2 years 2 Math Class VIII 5 Question Bank 12.
x × 11 × 2
= Rs = Rs
1 2
100 x × 11 × 5 100 × 2
x × 11 ×
= Rs
= Rs
100 x × 11× 1 20 × 2
5 2 = Rs
11 x 40
Z L B A A N L I O U A T D N E
1 Simple interest on Rs x at 9.5% for 1 years 2 3 1 x × 9.5 × x × 9.5 × 1 2 2 = Rs = Rs 100 100 5.7 x x × 9.5 × 3 x × 1.9 × 3 = Rs = Rs = Rs 100 × 2 20 × 2 40 As per given condition 11 x 5.7 x 11 x – 5.7 x = + 1590 ⇒ = 1590 40 40 40 5.3 x = 1590 5.3 x = 1590 × 40 ⇒ ⇒ 40 1590 × 40 = = 30 × 400 = 12000 x ⇒ 5.3 Hence, the some of money is Rs 12000.
©
13.
R E T N I
The simple interest on a certain sum of money is
3 8
of the sum
1 after 6 years. Find the rate per cent charged. 4 Ans. Let P = Rs 8 25 3 1 S. I. = Rs × 8 = Rs 3, T = 6 years = years 4 8 4 100 × I 100 × 3 100 × 3 4 = = × = 2 × 3 = 6% Now, R = 25 8 25 P×T 8× 4 14. How long will it take a certain sum of money to triple itself at 1 13 % per annum simple interest ? 3 Math Class VIII
6
Question Bank
Ans. Let the sum of money be Rs x
Amount = 3 × Rs x = Rs 3 x Interest = Amount – Principal = Rs 3 x – Rs x = Rs 2 x 40 1 % p.a. Rate = 13 % p.a. = 3 3 Time =
=
Z L B A A N L I O U A T D N E
I × 100
=
P×R
100 × 3
2 x × 100 years 40 x ×
=
2 × 100 × 3 40
years
3
years = 5 × 3 years = 15 years.
20 So, required time = 15 years. 15. At a certain rate of simple interest, Rs 4050 amounts to Rs 4576.50 in 2 years. At the same rate of interest, how much would Rs 1 lac amount to in 3 years ? Ans. Here, P = Rs 4050, A = Rs 4576.50, T = 2 years I = A – P = Rs 4576.50 – Rs 4050 = Rs 526.50
©
R E T N I
Let the rate of simple interest be R% per annum Then,
R
=
I × 100
=
526.50 × 100 4050 × 2
P×T
=
526.50 × 10
405 × 2 = 6.5% p.a. Now, P = Rs 1 lac = Rs 100000 R = 6.5% p.a. T = 3 years I=
P × R× T 100
=
Rs
% p.a.
% p.a. =
5265 810
% p.a.
100000 × 6.5 × 3
100 = Rs 1000 × 6.5 ×3 = Rs 19500
Amount = Principal + Interest = Rs 100000 + Rs 19500 = Rs 119500 Math Class VIII
7
Question Bank
16.
What sum of money lent at 9% for 3 years produces twice as much simple interest as Rs 4000 in 4 years 6 months at 12% per annum ? Ans. When P = Rs 4000, R = 12% 6 1 9 = = 4 4 T = 4 years, 6 months years years = years 12 2 2 9 4000 × 12 × P×R ×T 4000 × 12 × 9 2 I= = Rs = Rs 100 100 100 × 2 = Rs 40 × 6 × 9 = Rs 2160
Z L B A A N L I O U A T D N E
Double of this simple interest = 2 × Rs 2160 = Rs 4320 I = Rs 4320
R = 9% p.a. T = 3 years
P=
I × 100 R×T
=
4320 ×100
=
4320 × 100 27
9×3
R E T N I
= 160 × 100 = 16000
©
Hence, the sum of money lent = Rs 16000. 17.
A certain sum of money amounts to Rs 7650 in 4 years and to Rs 8100 in 6 years. Find the sum and the rate of simple interest.
Ans. Let
the sum of money be Rs x
and Rate of simple interest = R % per annum Case I:
P = Rs x, A = 7650, T = 4 years, Rate = R% P×R ×T We know that, A = P + 100 RT R × 4 ⇒ 7650 = P 1 + ⇒ = x 1 + 7650 100 100
R ⇒ 7650 = x 1 + 25
⇒
x 1 +
= 7650 25
R
…(i)
Case II
P = Rs x, A = Rs 8100, T = 6 years, R = R% p.a.
Math Class VIII
8
Question Bank
∴
A = P 1 +
RT
100
R× 6 ⇒ 8100 = x 1 + 100 3R x ⇒ 1 + = 8100 50
⇒
8100 = x 1 +
3 R
50
Z L B A A N L I O U A T D N E
…(ii)
Dividing (ii) by (i), we have
3R x 1 + 50 8100 = R 7650 x 1 + 25
3R 1 + 50 810 = R 765 1 + 25
⇒
⇒
R 3R 765 1 + = 810 1 + 50 25
⇒
765 +
⇒
©
2295R
–
50 25 2295R–1620R
⇒
⇒
810 +
25
=
810 – 765
=
45
50
⇒
810R
R E T N I
2295R
50 810R
=
R
=
R
=
45 × 45 ×
675R
⇒
=
50
45
50
675 2
=
27
5×
2 3
=
10 3
=
3
1 3
1 3 % p.a. ∴ 3 Now, substituting the value of R in (i), we have,
Rate of interest
x 1 +
Math Class VIII
=
10 = 7650 3 × 25 9
Question Bank
⇒
2 = 7650 3× 5
⇒
15 + 2 x = 7650 15
⇒
x 1 +
⇒ ⇒
2 = 7650 15 17 x = 7650 15 x 1 +
15
Z L B A A N L I O U A T D N E x = 7650 ×
17 x = 450 × 15
⇒
⇒
x = 6750
Hence, the sum of money = Rs 6750 18.
Mohini lent out Rs 7000 at 6% and Rs 9500 at 5%. Find her total income from the interest in 3 years. Ans.Case I P = Rs 7000 R = 6%, T = 3 years S.I. =
P ×R ×T 100
Case II:
©
= Rs
7000 × 6 × 3 100
= Rs 1260
R E T N I
P = Rs 9500, R = 5%,
T = 3 years S.I. =
P ×R ×T
9500 × 5 × 3
= Rs 1425 100 100 Total income from the interest = Rs (1260 + 1425) = Rs 2685. 19.
= Rs
Raj borrows Rs 8,000; out of which Rs 4500 at 5% and remainder at 6%. Find the total interest paid by him in 4 years
Ans. Total
sum borrowed by Raj = Rs 8000
Case I
P = Rs 4500, R = 5%, T = 4 years, = Rs
4500 × 5 × 4 100
= Rs 900
Case II
P = Rs 8000 – Rs 4500 = Rs 3500, R = 6%, T = 4 years Math Class VIII
10
Question Bank
= Rs
3500 × 6 × 4
= 35 × 6 × 4 = Rs 840
100 Total interest paid by Raj = Rs (900 + 840) = Rs 1740 20.
1 Mohan lends Rs 4800 to Sohan for 4 years and Rs 2500 to Shyam 2 for 6 years and receives a total sum of Rs 2196 as interest. Find the rate per cent per annum, it being the same in both the cases.
Ans. Case I
Z L B A A N L I O U A T D N E 1
9
P = Rs 4800, R = x% (Suppose), T = 4 years = years 2 2 Interest =
P × R×T 100
= Rs Case II
©
4800 × x × 9 100 × 2
=
Rs 24 × x × 9 = Rs 216 x
R E T N I
P = Rs 2500, R = x %, T = 6 years = Rs
2500 × x × 6
=
Rs 25 × x × 6 = Rs 150 x
100 According to the given condition Interest in first case + Interest in second case = Rs 2196 Rs (216 x + 150 x) = Rs 2196 Rs 366 x = Rs 2196 ⇒
⇒
x =
2196
=
732
⇒ x = 6
366 122 Hence, rate of interest is 6%. 21. A lends Rs 2500 to B and a certain sum to C at the same time at 7% per annum simple interest. If, after 4 years, A altogether receives Rs 1120 as interest from B and C , find the sum lent to C . Form B, Ans. Sum (P) = Rs 2500, Rate ( R) = 7% p.a., Period (t ) = 4 years. Math Class VIII
11
Question Bank
P×R×T
Thus, Simple Interest =
=
2500 × 7 × 4 100
100 Total interest received by A = Rs 1120
= Rs 700
From C , Interest from C = Rs 1120 – 700 = Rs 420 ∴
Z L B A A N L I O U A T D N E
Rate (R) = 7% and period (T) = 4 years S.I. × 100 420 ×100 = Thus, sum = = Rs 1500 R ×T 7×4 Hence, sum lent to C = Rs 1500. 22.
The simple interest on a certain sum for 3 years at 8% per annum is Rs 96 more than the simple interest on the same sum for 2 years at 9% per annum. Find the sum. Ans. Let sum in each case be Rs x Case I
Rate (R) = 8% p.a.,
Period (T) = 3 years P×R ×T Thus, simple interest = 100
©
Case II
R E T N I
×
=
8×3
=
100
24 x
100
Sum = x, Rate = 9% p.a, Period = 2 years Thus, Simple interest =
x × 9 × 2
=
18 x
100 100 According to the given condition 24 x 100
–
18 x 100 6 x
=
96
=
96
⇒
x
=
96 × 100
=
1600
6 100 Hence, sum in each case is Rs 1600. 23. Divide Rs 6000 into two parts so that the simple interest on the first part for 9 months at 12% per annum is equal to the simple 1 interest on the second part for 1 years at 10% per annum. Math Class VIII 12 2 Question Bank
Ans. Total
sum = Rs 6000
Let first part be x then second part = (6000 – x). Simple interest on first part for 9 months at 12% p.a. 9 x × 12 × 9 =
=
100 × 12 100 1 and interest on second part for 1 years at 10% p.a. 2 (6000 – x ) × 10 × 3 15(6000 – x )
Z L B A A N L I O U A T D N E =
=
100 × 2 According to the given condition 9 x
=
100
15(6000 – x )
100 100 9 x = 15 (6000 – x)
⇒ ⇒
⇒
9 x + 15 x = 90000
Thus,
©
x
=
90000
R E T N I 24
=
24 x = 90000
3750
Hence, first part of sum is Rs 3750 and second part is Rs (6000 – 3750) = Rs 2250 24. Divide a sum of Rs 13500 into two parts such that if one part be 1 lent at 8 % per annum for 2 years 9 months and the other at 3 1 7 % per annum for 1 year 8 months, the total interest received is 2 Rs 2375. Ans. Total sum = Rs 13500 Let first part be x. Then, second part = Rs (13500 – x) 1 In first part the simple interest for 2 years 9 month at 8 % p.a. 3 1 x × 8 × 2 years 9 months 275 x × 25 × 11 3 =
=
100 Math Class VIII
=
100 × 3 × 4 13
1200 Question Bank
1 Simple Interest in second case for 1 year 8 months at 7 % p.a. 2 1 (13500 – x) × 7 × 1year 8months 2 = 100 (13500 – x) × 15 × 5 75(13500 – )
Z L B A A N L I O U A T D N E =
=
100 × 2 × 3
Total interest = Rs 2375 275 x 75(13500 – x) ∴
⇒
+
1200 600 275 x + 150(13500 – x)
=
600
2375
=
2375
1200 ⇒ 275 x + 2025000 – 150 x = 2375 × 1200 125 x = 2850000 – 2025000 ⇒ 125 x = 825000 ⇒ 825000 = = 6600 x ⇒ 125 Thus, First part = Rs 6600 and Second part = Rs 13500 – 6600 = Rs 6900. 25. John lent Rs 2550 to Mohan at 7.5 per cent. If Mohan discharges the debt after 8 months by giving an old black and white television and Rs 1422.50; find the price of the television. Ans. P = Rs 2550, R = 7.5% 8 2 T = 8 months = years = years 12 3 2 1 P ×R ×T × S.I. = = Rs 2550 × 7.5 × 3 100 100 2550 × 7.5 × 2 2550 × 5 = Rs = Rs 3 × 100 100 12750 = Rs = Rs 127.50 100 Amount = P + I = Rs (2550 + 127.50) = Rs 2677.50
©
Math Class VIII
R E T N I
14
Question Bank
Mohan paid in cash = Rs 1422.50 Price of the television = amount – paid in cash = Rs 2677.50 – 1422.50 = Rs 1255 A sum of money lent at 2% per annum simple interest for 5 years yields a certain amount of interest. If lent for 7 years, it would have yielded Rs 12 more interest. Find the sum of money. Ans. Let the sum of money be Rs x Rate = 2% p.a., Time = 5 years 26.
Z L B A A N L I O U A T D N E I = Rs
x × 2 × 5
100
= Rs
x
10
Also, when time = 7 years I=
P×R ×T 100
= Rs
x × 2 × 7
14 x
=
100
100
As per as given condition 14 x 100
x
=
+
10
©
⇒
R E T N I
⇒
14 x – 10 x
⇒
x = 12 ×
100
12
=
12
100
–
100
⇒
x
10 4 x
⇒
4 Hence, the sum of money is Rs 300 27.
14 x
=
=
100
12
12
x = 3 × 100 = 300
7 How long will it take for a certain sum of money to amount to 5 of itself at the rate of 7.5% per annum simple interest ?
Ans. Let
the sum of money be Rs x.
Then amount =
7
7
of (sum of money) = Rs 5 5 Interest = Amount – Prinicipal
7 x – x – = Rs Rs x = Rs = Rs 5 5 7 x
× x =
Rs
7 x 5
2 7 x – 5 x = Rs 5 5
Rate = 7.5% p.a. Math Class VIII
15
Question Bank
2 x T=
28.
×
5
100 years
=
2 x × 100
years
=
2 × 100
years
5 × 7.5 5 × x × 7.5 2 × 100 × 10 2× 4× 2 16 1 5 = = = years years years = years 5 × 75 1× 3 3 3 12 = 5 years months = 5 years and 4 months 3 Find the amount and the compound interest on Rs 5000 for 2 years at 8% per annum, compounded annually. x × 7.5
Ans. Principal
Z L B A A N L I O U A T D N E
for the first year = Rs 5000
5000 × 8 ×1 Interest for first year = Rs = Rs 400 100
Amount at the end of the first year = (5000 + 400) Principal for second year = Rs 5400
©
5400 × 8 ×1 = Rs 432 100
R E T N I
Interest for second year = Rs
Amount at the end of second year ∴
= Rs 5000 + 400 + 432 = Rs 5832
Amount = Rs 5832
Compound Interest = (Total Amount – Principal) = Rs (5832 – 5000) = Rs 832
29.
Find the amount and the compound interest on Rs 2500 for 2 years, compounded annually, the rate of interest being 6% during the first year and 8% during second year.
Ans. Principal
for the first year = Rs 2500
2500 × 6 ×1 = Rs 150 100
Interest for first year = Rs
Principal for second year = Rs (2500 + 150) = Rs 2650 Math Class VIII
16
Question Bank
2650 × 8 ×1 Interest for second year = Rs 100 265 × 4
1060
Rs 212 5 5 Amount at the end of second year = Rs (2650 + 212) = Rs 2862 =
=
=
Z L B A A N L I O U A T D N E
Compound Interest = Rs (2862 – 2500) = Rs 362
Find the compound interest on Rs 14000 for 2 years at the rate of 5% per annum. Ans. Rate of interest = 5% per annum. Principal for the first year = Rs14000 30.
Interest for the first year = Rs
14000 × 5 × 1
= Rs 700 100 Amount at the end of first year = Rs 14000 + Rs 700 = Rs 14700 Principal for the 2nd year = Rs 14700 14700 × 5 × 1 Interest for the 2nd year = Rs = Rs 735 100 Amount at the end of 2nd year = Rs 14700 + Rs 735 = Rs 15435 Compound interest for 2 years = Final amount ∴ – (original) Principal = Rs 15435 – Rs 14000 = Rs1435 31. Jacob invests Rs 12000 for 3 years at 10% per annum. Calculate the amount and the compound interest that jacob will get after 3 years. Ans. Principal for the 1st year = Rs 12000 Rate = 10% p.a.
©
R E T N I
Interest for the 1st year = Rs
12000 × 10 × 1 100
= Rs1200
Amount at the end of 1st year = Rs 12000 + Rs 1200 = Rs 13200 Principal for the 2nd year = Rs 13200 Interest for the 2nd year = Rs Math Class VIII
13200 × 10 × 1
17
100
= Rs 1320 Question Bank
Amount at the end of 2nd year = Rs 13200 + 1320 = Rs 14520 Principal for the 3rd year = Rs14520 Interest for the 3rd year = Rs
14520 × 10 × 1 100
= Rs 1452
Amount at the end of 3rd year = Rs 14520 + Rs 1452 = Rs 15972
Z L B A A N L I O U A T D N E
Compound interest for 3 year = Final amount – (original) Principal = Rs 15972 – Rs 12000 = Rs 3972
©
Math Class VIII
R E T N I
18
Question Bank
