Class 8 ICSE Maths Solutions Chapter 9 Interest (Selina Concise)
Welcome to NCTB Solutions. Here with this post we are going to help 8th class students for the Solutions of Selina Class 8 ICSE Math Book, Chapter 9, Interest (Simple and Compound). Here students can easily find step by step solutions of all the problems for Interest (Simple and Compound), Exercise 9A, 9B and 9C Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get chapter 9 solutions. Here in this post all the solutions are based on ICSE latest Syllabus.
Interest (Simple and Compound) Exercise 9(A) Solution :
Question no – (1)
Solution :
(i) As per the question,
Principal = 750;
Time = 3 4/12
= 3 1/3
= 10/3 years
Rate = 10%
∴ Simple Interest = PRT/100
= 750 × 10 × 10/3 × 100
= 250
∴ Now, the Amount,
= (750 + 250)
= 1000 Rs
Therefore, Interest is Rs 250 and amount will be 1000 Rs.
(ii) Given, Principal = 5000 Rs
And, Rate = 8%
From 23rd December to 29th July,
= (8 + 31 + 29 + 31 + 30 + 31 + 30 + 29)
= 219 days
= Times = 219/365 years
∴ Interest,
= 5000 × 8 × 219/100 × 365
= 240 Rs
∴ Amount,
= (5000 + 240)
= 5240 Rs
Therefore, the interest is 240 and amount will be 5240 Rs.
(iii) Given, Principal = 2600 Rs
Time = 2 years 3 m = (2 × 12) + 3 = 27 months
Rate = 1%
∴ Interest,
= 2600 × 27 × 1/100
= 702 Rs
∴ Amount,
= (2600 + 702)
= 3302 Rs
Thus, the interest is 702 and the amount is 3302 Rs.
(iv) From the question we get,
Principal = 4000 Rs
Time = 1 1/3 = 4/3 = 4/3× 12 = 16 month
Rate = 2%
∴ Interest,
= 4000 × 2 × 16/100
= 1280 Rs
∴ Amount,
= (4000 + 12800)
= 5280 Rs
Therefore, the interest will be 1280 and the amount will be 5280 Rs.
Question no – (2)
Solution :
Simple Interest,
= 24000 × 4 × 7.5/100
= 7200 Rs
∴ Amount to be clear at the end of 4th years,
= (24000 + 7200)
= 31,200 Rs
Therefore, he will pay 31,200 at the end of 4 years to clear his debt.
Question no – (3)
Solution :
Let, principal = x
Time = 2 year
Rate = 10%
∴ Interest,
= x × 10 × 2/100 = x/5
∴ = x = (5 × 1480)
= 7400 Rs
Therefore, the sum of money will be 7400 Rs.
Question no – (4)
Solution :
Let, principal ‘P’
Time = 6 years 3 m
= (6 + 3/12) year
= 75/12
= 25/4 year.
Rate = 5%
Simple Interest = 7008 Rs
∴ Simple Interest = P × 25/4 × 5/100
= 7008 = R × 25/4 × 5/100
∴ P = 7008 × 100 × 4/25 × 5
= 112128/5
= 22425.60 Rs.
Therefore, the required principal will be 22425.60 Rs.
Question no – (5)
Solution :
Let, Principal = p;
Time = 4 years
Rate = 6 1/4
= 25/4%
∴ S.I = P × 25/4 × 4/100
= P/4
∴ Amount = (p + p/4)
= 5p/4
5p/4 = 4000
= P = 4 × 4000/5
= 3200 Rs
Therefore, the principal will be 3200 Rs.
Question no – (6)
Solution :
(i) Given, Principal = 630 Rs
Interest = 126 Rs
Time = 4 years
∴ Rate = 100 × 126/630 × 4
= 5%
Hence, the rate percent will be 5%.
(ii) Let, Principal = 100 Rs
Amount = (2 × 100)
= 200 Rs
∴ Interest,
= (200 – 100)
= 100 Rs
∴ Time = 6 1/4 years
= 25/4 years
∴ Rate = 100 × 100/100 × 25/4
= 100 × 100 × 4/100
= 16%
Therefore, the Rate of Interest will be 16%
Question no – (7)
Solution :
(i) Given in the question,
Principal = 950 Rs
Simple Interest = 399 Rs
∴ Time,
= 100 × 399/950 × 7
= 6 years.
Therefore, the required time will be 6 years.
(ii) Given, Amount = 1536 Rs
And, Principal = 1200 Rs
Interest = (1536 – 1200)
= 336 Rs
We know that,
Time = 100 × 336/1200 × 3.5
= 8 years
Hence, the required time will be 8 years.
Question no – (8)
Solution :
Let, principal = 8 Rs
Simple Interest = (3/8 × 8)
= 3 Rs
Time = 6 1/4
= 25/4 years
∴ Rate = 100 × 3/8 × 25/4
= 100 × 3 × 4/8 × 25
= 6%
Therefore, the rate percent will be 6%.
Question no – (10)
Solution :
Let, p = 8 Rs
Interest = (8 × 5/8)
= 5 Rs
∴ Time = 100 × 5/8 × 6
= 125/12 years
= 10 5/12
= 10 years 5 months.
Therefore, the required time will be 10 years 5 months.
Question no – (11)
Solution :
At 1st, S.I. = 7000 × 6 × 3/100
= 1260
2nd, S.I. = PRT/100
= 9500 × 5 × 3/100
= 1424 Rs.
∴ Total income,
= (1260 + 1425)
= 2685
Therefore, Ashok total income from the interest in 3 years will be 2685 Rs.
Question no – (12)
Solution :
1st, S.I. = 4500 × 5 × 4/100
= 900 Rs
2nd, P = (8000 – 4500)
= 3500 Rs
Given Rate = 6%
S.I. = 3500 × 6 × 4/100
= 840 Rs
∴ Total interest paid,
= (900 + 8400
= 1740 Rs
Therefore, the total interest will be 14740 Rs.
Question no – (13)
Solution :
At first case,
Let, Rate = x%
Time = 4 1/2 years
= 9/2
∴ Interest
= 4800 × x × 9/100 × 2
= 216x
2nd case,
Interest = PRT/100
= 2500 × x × 6/100
= 150x
Now, 216x + 150x = 2196
= 366x = 2196
= x = 2196/366
= 6%
Hence, the rate percent per annum will be 6%.
Question no – (14)
Solution :
Here, Time = 8 months
= 8/12
= 2/3 years
S.I = 2550 × 7.5 × 2/3/100
= 2550 × 7.5 × 2/3 × 100
= 127.50 Rs
Now the Amount,
= (2550 + 127.50)
= 2677.50 Rs
∴ Price of television,
= (2677.50 – 1422.50)
= 1255 Rs
Therefore, the price of the television will be 1255 Rs.
Interest (Simple and Compound) Exercise 9(B) Solution :
Question no – (1)
Solution :
As per the given question,
Let, sum = 100 Rs
Time = 3 years
Rate of interest = r%
∴ Interest = 100 × 3 × r/100
= 3r
= (0.24) × 100 = 3r
= r = 24/3
= 8%
Hence, the rate of interest will be 8%.
Question no – (2)
Solution :
Here, p = 3750 Rs
Amount = 4620 Rs
∴ Interest,
= (4620 – 3750)
= 870 Rs
Time = 3 years
Rate = 100 × 870/3750 × 3
= 100 × 290/3750
= 116/15
= 7 11/15%
Now, P = 7500;
Rate = 116/15
= 7 11/15%
Time = 5 1/2 years
= 11/2 years
∴ Interest,
= 7500 × 11 × 116/2 × 15 × 100
= 3190 Rs
∴ Now the Amount,
= (7500 + 3190)
= 10,690 Rs
Therefore, the rate of interest will be 7 11/15% and amount will be 10,690 Rs.
Question no – (4)
Solution :
First, Amount = 5000 Rs
Principal = 4000 Rs
Interest = (5000 – 4000) = 1000 Rs
Time = 8 years
∴ Rate = 100 × I/P × R
= 100 × 1000/4000 × 8
= 25/8%
2nd, Amount = 2800
Principal = 2100
Interest = (2800 – 2100)
= 700 Rs
∴ Rate = 25/8%
∴ Time = 100 × 7000 × 8/2100 × 25
= 32/3 years
= 10 2/3 years
= 10 years 8 months.
Hence, the required time will be 10 years 8 months.
Question no – (5)
Solution :
1st, Principal = 7500 Rs
Rate = 5%
Time = 6 years
∴ Interest = PRT/100
= 7500 × 5 × 6/100
= 2250 Rs
2nd, case,
Rate = 6.5%;
Time = 4 years
Interest = 2250 Rs
∴ Principal,
= 100 × 2250/6.5 × 4 …[From P = 100×I/R×T]
= 8653.25 Rs
Hence, the required sum of money will be 8653.25 Rs
Question no – (6)
Solution :
As per the given question,
In 6 years Amount = 4050
4 years Amount = 3825
Interest of 2 years
= (4050 – 3825)
= 225 Rs
Interest of 4 years
= (225/2 × 4)
= 450 Rs
Principal,
= (3825 – 450)
= 3375 Rs
Now, Rate = 100 × 450/3375 × 4
= 90/3
= 3 1/3%
Therefore, the rate percent will be 3 1/3% and sum will be 3375 Rs.
Question no – (7)
Solution :
Here, Rate = 100 × I/P × T
= 100 × 750/3750 × 4
= 5%
Now, Interest of 4 years = 750
∴ Interest of 15 years = (750/4 × 15)
= 2812.50
So, Amount in 15 years will be,
= (3750 + 2812.50)
= 6562.50 Rs
Therefore, the rate will be 5% and amount in 15 years will be 6562.50 Rs.
Question no – (8)
Solution :
Interest = (A – P)
= (2125.50 – 1950)
= 175.50 Rs
Time = 100 × I/P× R
= 100 × 175.50/1950 × 5
= 9/5
= 1 4/5
= 1 year 4/5 × 365
= 1 year 292 days
So, Now required date,
= (31 – 5) + 29 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 23
= 292 days.
Therefore, the required date will be 23rd October.
Question no – (9)
Solution :
At 1st, Let, R = x %
So, I = PRT/100
= 2400 × x × 3/100
= 72 x
2nd, Interest = 2000 × x × 3/100
= 60x
So, 72x = 60x + 60
= 72x – 60x = 60
= 12x = 60
= x = 5% [60/12 = 5]
Therefore, the rate will be 5%.
Question no – (10)
Solution :
Let, 1st part, x
2nd part = (15600 – x)
So, x × 5 × 5/100 = (16500 – x) × 9/2 × 6/100
= 25x = 27 × 15600 – 27x
= 25x + 27x = 27 × 15600
= x = 27 × 15600/52
= 8100 Rs
∴ 1st, part = 8100 Rs
∴ 2nd, part = (15600 – 8100)
= 7500 Rs
Interest (Simple and Compound) Exercise 9(C) Solution :
Question no – (1)
Solution :
(i) Interest for the first year,
∴ Interest of 1st year
= 8000 × 10 × 1/100
= 800 Rs
(ii) Principal for the second year,
Amount = (8000 + 800)
= 8800 Rs
∴ Principal of 2nd years = 8800 Rs
(iii) Interest for the second year,
∴ Interest for 2nd year
= 8800 × 10 × 1/100
= 880 Rs
(iv) Final amount at the end of the second year,
∴ Amount at the end of 2nd year,
= (8800 + 880)
= 9680 Rs
(v) Compound interest earned in 2 years,
∴ Compound Interest in 2 years,
= (9680 – 8000)
= 1680 Rs
Question no – (2)
Solution :
(i) The interest of the first year.
= 20,000 × 8 × 1/100
= 1600 Rs
(ii) the interest of the second year.
Amount after 1 year,
= (20,000 + 1600)
= 21,600 Rs
∴ Interest of 2nd year,
= 21600 × 8 × 1/100
= 1728 Rs
(iii) the final amount at the end of the second year.
Final amount at the end of the year,
= (21600 + 1728)
= 23,328 Rs
(iv) the compound interest of two years.
Interest of two years,
= (23,328 – 20,000)
= 3,328 Rs
Question no – (3)
Solution :
1st year Interest,
= 12000 × 10 × 1/100
= 1200 Rs
1st year Amount,
= (12000 + 1200)
= 13200 Rs
2nd year, Interest
= 13200 × 10 × 1/100
= 1320 Rs
Amount in 2 years,
= (13200 + 1320)
= 14520 Rs
And, C.I of two years,
= (1200 + 1320)
= 2520 Rs
Question no – (4)
Solution :
Amount after 3 years,
= 10,000 (1 + 8/100)³
= 10,000 × (108/100)³
= 10,000 × 108 × 108 × 108/100 × 100 × 100
= 12597.12 Rs
∴ Now the Compound Interest,
= (12597.12 – 10,000)
= 2597.12 Rs
Therefore, the amount will be 12597.12 Rs and Compound Interest will be 2597.12 Rs.
Question no – (5)
Solution :
Amount in two years,
= 5000 (1 + 10/100) (1 + 12/100)
= 5000 × (100 + 10/100) (100 + 12/100)
= (5000 × 110/100 × 112/100)
= 6160 Rs.
∴ Compound Interest,
= (6160 – 5000)
= 1160 Rs.
Hence, the compound interest will be 1160 Rs.
Question no – (6)
Solution :
Amount in 3 years,
= 15000 (1 + 6/100) (1 + 8/100) (1 + 10/100)
= 15000 × 106/100 × 108/100 × 110/100
= 18829.20 Rs
∴ Compound Interest,
= (18829.20 – 15000)
= 3829.2 Rs
Therefore, the amount will be Rs 18829.20 and compound interest will be Rs 3829.2.
Question no – (7)
Solution :
Amount paid after 3 years,
= 16000 (1 + 5/100)³
= 16000 (100 + 5/100)³
= 16000 × 105/100 × 105/100 × 105/100
= 18522 Rs
Thus, Mohan have to pay Rs. 18522 at the end of three years.
Question no – (8)
Solution :
Amount after 2 years,
= 40,000 (1 + 10/100)²
= 40,000 × (100 + 10/100)²
= 40,000 × (110/100)²
= 40,000 × 110 × 110/100 × 100
= 48,400 Rs
∴ Compound Interest,
= (48400 – 40000)
= 8,400 Rs
Therefore, interest pay by Rekha in the second years will be 8400 Rs.
Question no – (9)
Solution :
Amount after 2 years,
= 15000 (1 + 6/100)²
= 15000 (1000 + 6/100)²
= 15000 (106/100 × 106/100)
= 16854 Rs
Compound Interest in two years,
= (16854 – 15000)
= 1854
For 1st year Compound Interest,
= (15000 × 6/100)
= 900 Rs
And 2nd years Compound Interest,
= (15000 + 900) × 6/100
= (15900 × 6/100)
= 954 Rs
Therefore, the compound interest for 2nd years will be Rs. 954
Question no – (10)
Solution :
(i) the interest for the first year.
Interest of 1st year,
= (9600 × 10/100)
= 960 Rs
(ii) the amount at the end of the first year.
Amount at the end of 1st year
= (960 + 9600)
= 10560 Rs
(iii) the interest for the second year.
Interest at 2nd year,
= 10560 × 10 × 1/100
= 1056 Rs
Amount after 2nd year,
= (10560 + 1056)
= 11616 Rs
(iv) the interest for the third year.
The interest at third year,
= 11616 × 10 × 1/100
= 1161.00 Rs
Question no – (11)
Solution :
Here, P = 5000 Rs
Time = 2 year
Amount at end of 1 year = 5600
∴ Interest,
= (5600 – 5000)
= 600 Rs
(i) Rate of interest per annum,
= 600 × 100/5000 × 1
= 12%
(ii) the amount at the end of the second year.
Principal 2nd year = 5600 Rs
∴ Interest,
= 5600 × 12 × 1/100
= 672 Rs
∴ Amount at the end of 2nd year,
= (5600 + 672)
= 6272 Rs
Question no – (12)
Solution :
As per the question we know,
Principal = 7500 Rs
Rate = 8%
Time = 2 year
Simple Interest = 7500 × 8 × 2/100
= 1200 Rs
Interest,
= 7500 × 8 × 1/100
= 600 Rs
Amount = (7500 + 600)
= 8100 Rs
2nd year, principal = 8100
∴ Interest,
= 8100 × 8 × 1/100
= 648 Rs
Total CI for 2 years,
= (600 + 648)
= 1248 Rs
Difference between C.I and S.I for 2 years,
= (1248 – 1200)
= 48 Rs
Therefore, the difference between C.I and S.I will be 48 Rs
Question no – (13)
Solution :
Here, principal = 8000 Rs
Rate = 10%
Time = 3 years.
∴ Simple Interest of 3 years,
= 8000 × 10 × 3/100
= 2400 Rs
And, Simple Interest of 1 year = 2400/3
= 800 Rs
Amount of 1st year
= (8000 + 800)
= 8800 Rs
In 2nd year principal = 8800
Interest of 2nd year
= 8800 × 10 × 1/100
= 880 Rs
Amount = (8800 + 880)
= 9680 Rs
3nd year, Interest
= 9680 × 10 × 1/100
= 968 Rs
∴ Compound Interest for 3 years,
= (800 + 880 + 968)
= 264 Rs
∴ Difference between Compound Interest and Simple Interest for 3 years,
= (2648 – 2400)
= 248 Rs
Hence, the difference between S.I and C.I will be Rs. 248
Question no – (14)
Solution :
According to the question we know,
Principal = 40,000
Rate = 10%
Time = 2 years
∴ Now the Interest,
= 40,000 × 10 × 1/100
= 4000 Rs
∴ The amount will be,
= (40,000 + 4000)
= 44,000 Rs
2nd years, principal = 44000
Interest = 44000 × 10 × 1/100
= 4400 Rs
∴ C.I of 2 years,
= (4000 + 4400)
= 8400 Rs
Therefore, Both case interest will Same.
Question no – (15)
Solution :
Here, Principal = 24000 Rs
Rate = 13%
Time = 2 years
∴ Simple Interest of 2 years,
= 24000 × 13 × 2/100
= 6240 Rs
In 12% Compound Interest,
= 24000 × 12 × 1/100
= 2880 Rs
∴ Amount after 1st year,
= (24000 + 2880)
= 26880 Rs
∴ Interest,
= 26880 × 12 × 1/100
= 3225.60 Rs
Compound Interest of 2 years,
= (2880 + 3225.60)
= 6105.60 Rs
∴ Total interest,
= (6240 + 6105.60)
= 12345.60 Rs
Thus, total interest earned by Mr. Sharma in 2 years will be 12345.60 Rs
Question no – (16)
Solution :
Sum borrowed = 12000 Rs
Rate = 10%
Time = 2 years
∴ The Interest will be,
= 12000 × 10 × 1/100
= 12000 Rs
(i) Amount,
= (12000 = 1200)
= 13200 Rs
(ii) Balance amount,
= (13200 – 8000)
= 5200 Rs
(iii) Interest of 2nd years,
= 5200 × 10 × 1/100
= 520 Rs
∴ Amount,
= (5200 + 520)
= 5720 Rs
Question no – (17)
Solution :
Loan taken = 16000 Rs
Rate = 15%
Time = 2 years
∴ The Interest will be,
= 16000 × 15 × 1/100
= 2400 Rs
Amount,
= (16000 = 2400)
= 18400 Rs
Balance,
= (18400 – 9000)
= 9400 Rs
Interest of 2nd years,
= (9400 × 15 × 1/100)
= 1410 Rs
∴ Amount of 2nd years,
= (9400 + 1410)
= 10810 Rs
Therefore, he must be pay 10810 Rs at the end of second year.
Question no – (18)
Solution :
As per the given question,
Rate = 8%
Time = 5 years
Interest = 12000 Rs
(i) Sum = I × 100/R × T
= 12000 × 100/8 × 5
= 30.000 Rs
(ii) Rate = 10%
Time = 2 years
∴ Interest = 30,000 × 10 × 1/100
= 3000 Rs
Amount,
= (30,000 + 3000)
= 33,000 Rs
Interest 2nd years
= 33000 × 10 × 1/100
= 3300 Rs
∴ Compound Interest of 2nd years,
= (3000 + 3300)
= 6300 Rs
Therefore, the sum of money will be Rs 33,000 and Compound Interest will be 6300 Rs.
Question no – (19)
Solution :
Given in the question,
P = 12,000
R = 10%
T = 1 year
∴ Amount = 12000 (1 + 10/2 × 100)²
= 12000 (1 + 10/200)²
= 12000(200 + 10/200)²
= 12000 (210/200)²
= 12000 × 210 × 210/200 × 200
= 13,230 Rs
∴ Compound Interest,
= (13230 – 12000)
= 1230 Rs
Therefore, the amount will be Rs 13,230 and compound interest will be Rs 1230.
Question no – (20)
Solution :
As per the question,
P = 8000 Rs
R = 20%
T = 1 1/2 = 3/2
∴ Amount = 8000 (1 + 20/2 × 100) 3/2 × 2
= 8000 (200 + 20/200)³
= 8000 × (220/200)³
= 8000 × 22/20 × 22/20 × 22/20
= 10648 Rs
∴ Compound Interest,
= (10648 – 8000)
= 2648 Rs
Thus, the amount is 10,648 and compound interest is 2648 Rs.
Question no – (21)
Solution :
From the given question we get,
P = 24000
R = 10%
T = 2 years
∴ Amount = 24000 (1 + 10/2 × 100) 2 × 2
= 24000 × (1 + 10/200)⁴
= 24000 × (200 + 10/200)⁴
= 24000 × (210/200)⁴
= 24000 × 21/20 × 21/20 × 21/20 × 21/20
= 29172
∴ Compound Interest,
= (29172 – 24000)
= 5172
Therefore, the amount is 29,172 and compound interest is 5172 Rs.
Question no – (22)
Solution :
In the question we get,
P = 16,000 Rs
R = 5%
T = 3 years
∴ Amount = 16000 (1 + 5/2 × 100)2n
= 16000 (1 + 5/200) 3 × 2
= 16000 (200 + 5/200)⁶
= 16000 (205/200)⁶
= 16000 × 41/40 × 41/40 × 41/40 × 41/40 × 41/40 × 41/40
= 18,555 Rs
∴ Compound Interest,
= (18555 – 16000)
= 2555 Rs
Hence, the amount is 18,555 and compound interest is 2555 Rs.
Question no – (23)
Solution :
From the question we get,
P = 20,000
T = 1 1/2 years = 3/2
R = 10%
∴ Amount = 20,000 (1 + 10/2 × 100) 3/2 × 2
= 20,000 (1 + 10/200)³
= 20,000 (200 + 10/200)³
= 20,000 (210/200)³
= 20,000 × 21/20 × 21/20 × 21/20
= 23152.50
∴ Compound Interest,
= (23152.50 – 20,000)
= 3152.50
Therefore, the amount is 23152.50 and compound interest will be 3152.50.
Question no – (24)
Solution :
Given in the question,
P = 32000
T = 1 year
R = 20%
∴ Amount = P (1 + 20/2 × 100)2 × 1
= 32000 (1 + 20/200)²
= 32000 (200 + 20/200)²
= 32000 × (220/200)²
= 32000 × 11/10 × 11/10
= 38,720 Rs
∴ Compound Interest,
= (38,720 – 32000)
= 6720 Rs
Therefore, the amount is 38,720 and compound interest will be 6720 Rs.
Question no – (25)
Solution :
In the question we get,
P = 4000
T = 2 years
R = 10%
OR r2 = 15%
∴ Amount = P (1 + r/100) (1 + r2/100)
= 4000 (1 + 10/100) (1 + 15/100)
= 4000 (100 + 10/100) (100 + 15/100)
= 4000 (110/100) × 115/100
= 4000 × 11/10 × 23/20
= 5060 Rs
∴ Compound Interest,
= (5060 – 4000)
= 10.60 Rs
Hence, the amount is 5060 and compound interest will be 10.60 Rs.
Question no – (26)
Solution :
According to the given question,
P = 10,000 Rs
t = 3 years
r1 = 10%
r2 = 15%
r3 = 20%
∴ Amount = 10,000 (1 + 10/100) (1 + 15/100) (1 + 20/100)
= 10,000 × 11/10 × 23/20 × 6/5
= 15,180 Rs
∴ Compound Interest,
= 15180 – 10,OOO
= 5180 Rs
Therefore, the amount will be 15,180 and compound interest will be 5180 Rs.
Next Chapter Solution :
👉 Chapter 10 👈
