WBBSE Solutions For Class 10 Maths Chapter 2 Simple Interest Exercise 2.2
Two friends together took a loan amount of Rs. 15,000 to run a business from a bank at the rate of simple interest of per annum. Let us write, by calculating, the interest they have to pay after 4 yrs.
Solution: Here principal (P) = Rs. 15,000
Rate (r) = 12%
Time (t) = 4 yrs.
∴ Interest (I) = \(\frac{Prt}{100}\)
= \(\text { Rs. } \frac{15000 \times 12 \times 4}{100}\)
= Rs. 7200
Question 2. Let us determine the interest of Rs. 2000 at the rate of simple interest per annum from 1st January to 26th May 2005.
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Solution: No. of days from 1st January to 26th May 2005.
Time = 31 + 28 + 31 + 30 + 25
= 146 days
= \(\frac{146}{365}\)
= \(\frac{2}{5}\) yrs.
Principal (P) = Rs. 2000
Rate (r) = 6%
Interest = \(\frac{Prt}{100}\)
= \(\text { Rs. } \frac{2000 \times 6 \times \frac{2}{5}}{100}\)
= Rs. 48.
Question 3. Let us determine the amount (principal along with Interest) of Rs. 960 at the rate of simple interest of annum for 1 yr 3 months.
Solution: Principal (P) = Rs. 960
Rate(r) = \(8 \frac{1}{3} \%=\frac{25}{3} \%\)
Time (t) = 1 yrs m = \(1 \frac{3}{12}=1 \frac{1}{4}=\frac{5}{4} \mathrm{yrs}\)
Interest (I) = \(\frac{\text { prt }}{100}=\text { Rs. } \frac{960 \times \frac{25}{3} \times \frac{5}{4}}{100}=\frac{80 \times 25 \times 5}{100}\)
= Rs. 100 Amount = Principal + Interest
= Rs. (960 + 100) = Rs. 1060.
Question 4. Utpalbabu took a loan of Rs. 3200 for 2 yrs. from a Cooperative bank for the cultivation of his land at the rate of simple interest per annum. Let us write by calculating the money she has deposited in the bank.
Solution: Here, Principal (P) = Rs. 3200
Rate (r) = 6%
Time (t) = 2 yrs.
Interest (I) = \(\frac{\text { Prt }}{100}=\text { Rs. } \frac{3200 \times 6 \times 2}{100}=\text { Rs. } 384\)
∴ Amount = Rs. (3200 + 384) = Rs. 3584.
Question 5. Sovadebi deposited some amount of money in a bank at the rate of simple interest of 5.25% per annum. After 2 yrs. she has got Rs. 840 as interest. Let us write by calculating the money she has deposited in the bank.
Solution: Here, Interest (I) = Rs. 840
Rate (r) = 5.25%
Time (t) = 2 yrs.
∴ Principal (P) = \(\frac{\text { Interest } \times 100}{\text { Rate } \times \text { Time }}\)
= \(\text { Rs. } \frac{840 \times 100}{5.25 \times 2}=\text { Rs. } \frac{840 \times 100 \times 100}{525 \times 2}\)
= Rs. 40 x 200 = Rs. 8000
∴ She deposited Rs. 8000.
Question 6. Goutam took a loan of some money from a Cooperative bank for opening a poultry farm at the rate of simple interest per annum. Every month he has to repay Rs. 378 as interest. Let us determine the loan amount taken by him.
Solution: Total Interest = Rs. 378
Rate = 12%
Time = \(\frac{1}{12}\) yrs.
Principal = \(\frac{\text { Interest } \times 100}{\text { Rate } \times \text { Time }}\)
= \(\text { Rs. } \frac{378 \times 100}{12 \times \frac{1}{12}}=\text { Rs. } 37800\)
∴ He takes loan of Rs. 37800.
Question 7. Let us write by calculating the number of years for which an amount becomes twice its principal having the rate of simple interest of per annum.
Solution: Let Principal = Rs. x
Rate = 60%
Interest = Rs. x
Time = ?
Time = \(\frac{\text { Interest } \times 100}{\text { Principal } \times \text { Rate }}\)
= \(\frac{x \times 100}{x \times 6}=16 \frac{2}{3} y r s .\)
∴ Time = \(16 \frac{2}{3} \mathrm{yrs}\)
Question 8. Mannan Miyan observed, after 6 years of taking a loan of some money, that the interest to be paid had become Th of its principal. Let us determine the rate of simple interest in percent per annum.
Solution: Let the principal = Rs. x
Interest = Rs. \(\frac{3 x}{8}\)
Time = 6 yrs, Rate = ?
Rate = \(\frac{\text { Interest } \times 100}{\text { Principal } \times \text { Time }}=\frac{\frac{3}{8} x \times 100}{x \times 6}\)
= \(\frac{3}{8} \times \frac{100}{6}=\frac{25}{4}=6 \frac{1}{4}\)
∴ Rate = \(6 \frac{1}{4}\) yrs.
Question 9. An agricultural Cooperative society gives agricultural loans to its members at the rate of simple interest per annum. But interest is to be given at the rate of simple interest per annum for a loan taken from the bank. If a farmer being a member of the Cooperative society takes a loan of Rs. from it instead of taking a loan from the bank, then let us write, by calculating, the money to be saved as interest per annum.
Solution: Principal = Rs. 5,000
Time = 1yr
Rate (1st case) = 4%
Rate (2nd case) = 7.4%
∴ saving in interest for 1 yr = (7.4 – 4) = 3.4%
∴ He saved Rs. 3.4 on Rs. 100.
i.e., on Rs. 100, Interest saved = Rs. 3.4
∴ On Rs. 5000 Interest saved = \(\frac{3.4}{100} \times 5000\)
= Rs. 34 x 5
= Rs. 170.
Question 10. If the interest of Rs. 292 in 1 day is 1 paise, then let us write by calculating the rate of simple interest in percent per annum.
Solution: Interest on Rs. 292 for 1 day = 5P
Interest on Rs 1 for 1 day = \(\frac{5}{292}\) P
Interest on Rs. 100 for 365 days = \(\frac{5}{292} \times 100 \times 365 \mathrm{P}\)
= Rs. \(\frac{25 \times 25}{100}\) = Rs. \(\frac{25}{4}\)
∴ Rate of interest = \(\frac{25}{4}=6 \frac{1}{4} \%\)
Question 11. Let us write by calculating the number of yrs. for which the interest of Rs. 600 at the rate of simple interest in percent per annum.
Solution: Principal (P) = Rs. 600
Rate (r) = 8%
Interest (I) = Rs. 168
Time = ?
Time = \(\frac{\text { Interest } \times 100}{\text { Principal } \times \text { Rate }}\)
= \(\frac{168 \times 100}{600 \times 8}=\frac{21}{6}=\frac{7}{2} \mathrm{yrs}=3 \frac{1}{2} \mathrm{yrs}\)
∴ Time = \(3 \frac{1}{2}\) yrs.
Question 12. If I get Rs. 1200 return as the amount (principal along with interest) by depositing Rs. 800 in the bank at the rate of simple interest of per annum, then let us write by calculating the time for which the money was deposited in the bank.
Solution: Amount = Rs. 120,
Principal = Rs. 800
Interest = Rs. (1200 – 800) = Rs. 400
Rate = 10%
Time = ?
∴ \(\text { Time }=\frac{\text { Interest } \times 100}{\text { Principal } \times \text { Rate }}\)
= \(\frac{400 \times 100}{800 \times 10}=5 y r s\)
∴ Time = 5 yrs.
Question 13. At the same rate of simple interest in percent per annum, if a principal becomes the amount of Ps. 7100 in 7 yrs and of Ps. 6200 in 4 yrs, let us determine the principal and rate of simple interest in percent per annum.
Solution: Principal + Interest for 7 yrs = Rs. 7100
Principal + Interest for 4 yrs = Rs. 6200
∴ Interest for 3 yrs = Rs. 900
Interest for 1 yrs = Rs. \(\frac{900}{3}\) = Rs. 300
Interest for 4 yrs interest = Rs. 300 x 4 = Rs. 1200
Principal + 4 yrs interest = Rs. 6200 + 4 yrs interest = Rs. 1200
∴ Principal = Rs. 5,000
Rate = \(\frac{\text { Interest } \times 100}{\text { Principal } \times \text { Time }}=\frac{1200 \times 100}{5000 \times 4}=6\)
∴ Rate = 6% & Principal = Rs. 5000.
Question 14. Amal Roy deposits Ra. 2000 in the bank and Pashupati Ghosh deposits Ra. 2000 in the post office at the same time. After 3 yrs. they get the return amounts Rs. 2360 and Let us write by calculating the ratio of the rate of simple interest in percent per annum in the bank and that in the post office.
Solution: In case of Amal Roy:
Principal = Rs. 2000
Interest = Rs. (2360 – 2000) = Rs. 360
Time = 3 yrs.
Rate = \(\frac{\text { Interest } \times 100}{\text { Principal } \times \text { Time }}\)
Rate = \(\frac{360 \times 100}{2000 \times 3}=6\)
In case of Pasipati chosh:
Principal = Rs. 2000
Interest = Rs. (2480 – 2000) = Rs. 480
Time = 3 years
Rate = \(\frac{\text { Interest } \times 100}{\text { Principal } \times \text { Time }}\)
= \(\frac{480 \times 100}{2000 \times 3}=8\)
∴ Ratio of Rate = 6 : 8 = 3 : 4.
Question 15. A weaver cooperative society takes a loan of Ris, 15,000 at the time of buying a power loom. After 5 yrs society has to repay As. 22125 for recovering the loan. Let us determine the rate of simple interest in percent per annum.
Solution: Principal = Rs 15,000
Interest = Rs. (22125 – 15,000) = Rs. 7125
Time = 5 years
Rate = \(\frac{\text { Interest } \times 100}{\text { Principal } \times \text { Time }}\)
= \(\frac{7125 \times 100}{15000 \times 5}\)
= \(\frac{1425}{150}=\frac{95}{10}=9.5\)
∴ Rate = 9.5%.
Question 16. Aslamehacha got Ra. 10,000 when he retired from his service. Ho deported some of that money to the post office and got Ra. 5400 in total per year as interest. If the rates of simple interest per annum in the bank and in the post office are and 64 respectively, then let us write by calculating the money he had deposited in the bank and post office.
Solution: Let he deposited Rs. x at the rate of 5% for 1 year in bank and he deposited Rs. (10,000 – x) at the rate of 6% for 1 year in post office. 1st case of Bank:
Interest = \(\frac{\text { Principal } \times \text { rate } \times \text { time }}{100}\)
= Rs. \(\frac{x \times 5 \times 1}{100}=\text { Rs } \frac{5 x}{100}\)
2nd case (In Post office)
Interest = \(\frac{\text { Principal } \times \text { rate } \times \text { time }}{100}\)
= \(\frac{{Rs}(100000-x) \times 6 \times 1}{100}\)
= \(\frac{{Rs}(100000-x) \times 6}{100}\)
According to the problem,
\(\frac{5 x}{100}+\frac{(10000-x) 6}{100}=5400\)= \(\frac{5 x+600000-6 x}{100}=6400\)
= -x + 600000 = 540000
60,0000 – 540000 = x
60000 = x
∴ He deposited Rs. 60,000in bank & Rs. {100000 – 60000} = Fis. 40,000 in post office.
Question 17. Relhadidi deposited Rs. 10,000 of her savings in two separate banks at the same time. The rate of simple interest per annum is of in one bank and that of In another bank; after 2 yrs, If she gets Rs. 1260 in total as interest, then let us write by calculating. the money she deposited separately in each of the two banks.
Solution: Let she deposited F = x in the 1st bank at the rate of 6% as (10000 – x) in the 2nd bank at the rate of 7% for 2 yrs.
According to the problem,
Rs. \(\left[\frac{\mathrm{x} \times 6 \times 2}{100}+\frac{(10000-\mathrm{x}) \times 7 \times 2}{100}\right]\) = Rs. 1280
or, \(\frac{12 \mathrm{x}}{100}+\frac{14(10000-\mathrm{x})}{100}=1260\)
or, \(\frac{12 x+140000-14 x}{100}=1280\)
or, -2x + 140000 = 1280 x 100
or, 140000 – 128000 = 2x
∴ \(x=\frac{12000}{2}=6000\)
∴ She deposited Rs. 6000 in the 18th bank & Rs. 4000 in the 2nd bark.
Question 18. A bank gives simple interest per annum. In that bank, Dipubabu deposits Rs. 15,000 at the beginning of the year, but withdraws Rs. 3000 after 3 months, and then again, after 3 months he deposits Rs. 8000 . Let us determine the amount (principal along with interest) Dipubabu will get at the end of the year.
Solution: Dipu babu’s total interest for 1 year
= \(\left[\frac{15000 \times 5}{100} \times \frac{3}{12}+\frac{12000 \times 5}{100} \times \frac{3}{12}+\frac{20000 \times 5}{100} \times \frac{6}{12}\right]\)
= Rs. \(\left[\frac{150 \times 5}{4}+150+500\right]\)
= Rs. [187.50 + 150 + 500] = Rs. 837.50
His amount will be Rs. [20000 + 837.50] = Rs. 20837.50.
Question 19. Rahamatchacha takes a loan amount of Rs. from a bank for constructing a building at the rate of simple interest of per annum. After of taking the loan, he rents the house at the rate of Rs. 5200 per month. Let us determine the number of yrs. he would take to repay his loan along with interest from the income of the house rent.
Solution: Let after x years he will repayment the amount.
Interest of Rs. 240000 at 12% for x years
= \(\frac{240000 \times 12 \times x}{100}=28800 x\)
Amount = Principal + Interest
= Rs. (240000 + 28800x)
Now, house rent for 1 year (12 m) = Rs. 5200 x 12
∴ House rent for (x – 1) yrs = Rs. 5200 x 12 x (x – 1)
= 62400(x – 1)
According to the problem,
62400(x – 1) = 240000 + 28800x
or, 62400x – 62400 = 240000 + 28800x
or, 62400x – 28800x = 240000 + 62400
or, 33600x = 302400
∴ \(x=\frac{302400}{33600}=9\)
∴ After 9 years he will repay his loan with interest.
Question 20. Rothinbabu deposits the money for each of his two daughters in such a way that when the age of each of his daughters will be 18 yrs., each one will get Rs, . The rate of simple interest per annum in the bank is and the present ages of his daughters are 13 yrs. and 8 yrs. respectively. Let us determine the money he had deposited separately in the bank for each of his daughters.
Solution: Let Rathin babu deposited Rs. x for his 1st daughter (13 yrs old) and he deposited Rs. y for his 2nd daughter (8 yrs old).
When his 1st daughter will be 18 yrs, old i.e., after (18 – 13) = 5 years
her amount = \(x+\frac{x \times 5 \times 10}{100}=120000\)
or, \(\frac{10 \mathrm{x} \times 5 \mathrm{x}}{10}=120000\)
or, 15x = 120000 x 10
or, \(x=\frac{1200000}{15}=80,000\)
When his 2nd daughter will be 18 years old, i.e., after (18 – 8) = 5 years
her amount = \(y+\frac{y \times 10 \times 10}{100}=2 y\)
∴ 2y = 120000
y = 60000
Chapter 2 Simple Interest Exercise 2.2 Multiple Choice Questions
Question 1. If the interest of Rs. p at the rate of simple interest of r% per annum in t years is I, then
1. I = prt
2. prt = 100 x 1
3. prt I = 100 x I
4. None of these
Solution: \(1=\frac{\text { prt }}{100} \text { or prt }=100 \times 1—-(\mathrm{c})\)
Question 2. A principal becomes twice of its amount in 20 yrs at a certain rate of simple interest. At the same rate of simple interest, that principal becomes thrice of its amount in
1. 30 yrs.
2. 35 yrs.
3. 40 yrs.
4. 45 yrs.
Solution: \(I=\frac{P r t}{100}\)
i.e., \(\mathrm{p}=\frac{{pr} \times 20}{100}\)
∴ r = 5
\(2 p=\frac{{Pr} t}{100}\)i.e., 2 x 100 = t x 5
∴ t = 40
Question 3. If a principal becomes twice its amount in 10 yrs., the rate of simple interest per annum is
1. 5%
2. 15%
3. 10%
4. 20%
Solution: \(I=\frac{\text { Prt }}{100}\)
i.e., \(\mathrm{p}=\frac{\mathrm{p} \times \mathrm{r} \times 10}{100}\)
∴ r = 10 ….(b)
Question 4. If the total Interest becomes Rs. x for any principal having the rate of simple Interest of x% per annum for x years then the principal will be
1. Rs. x
2. Rs 100/ X
3. Rs. 100x
4. Rs.100/x2
Solution: \(\mathrm{x}=\frac{\mathrm{px} \cdot \mathrm{x}}{100} \quad \mathrm{px}=100\mathrm{p}=\frac{100}{\mathrm{x}} \ldots \ldots \text { (c) }\)
Question 5. The total interest of a principal in n yrs. at the rate of simple interest of r% per annum is pnr/25 the principal will be
1. Rs. 2p
2. Rs. 4p
3. Rs. P/2
4. Rs. p/4
Solution: \(P=\frac{\mid \times 100}{r \times t}=\frac{p n r \times 100}{25 \times r \times n}=4 p\)
Chapter 2 Simple Interest Exercise 2.2 True or False
Question 1. A man who takes a loan is called a debtor.
Answer: True
Question 2. If the principal and the rate of simple interest in percent per annum be constants, then the total interest and the time are in inverse relation.
Answer: False
Chapter 2 Simple Interest Exercise 2.2 Fill In The Blanks
Question 1. A man who gives a loan is called
Answer: The man who gives a loan is called a money lender.
Question 2. The amount of Rs. 2p in t yrs. at the rate of simple interest per annum is Rs. (2p+————-)
Solution: Interest = \(\frac{2 \mathrm{p} \times \mathrm{t} \times \frac{\mathrm{r}}{2}}{100}=\frac{\mathrm{prt}}{100}\)
Amount = \(2 \mathrm{p}+\frac{\mathrm{prt}}{100}\)
Question 3. The ratio of the principal and the amount (principal along with interest) in 1 yr. is 8: 9; the rate of simple interest per annum is —————
Solution: Let the principal = Rs. 8x & the amount = Rs. 9x.
∴ Interest = Rs. x
∴ Rate = \(\frac{\text { Interest } \times 100}{\text { Principal } \times \text { Time }}\)
= \(\frac{x \times 100}{8 x \times 1}=\frac{25}{2}\)
∴ Rate = \(12 \frac{1}{2} \%\)
Chapter 2 Simple Interest Exercise 2.2 Short Answers
Question 1. Let us write the number of yrs. for which a principal becomes twice its amount having the rate of simple interest of 6 1/4% /9 per annum.
Solution: Let the principal = Rs. 100
∴ Amount = Rs. 200 and Interest = Rs. (200 – 100) = Rs. 100
Rate = \(6 \frac{1}{4} \%=\frac{25}{4} \%\)
∴ Time = \(\frac{\text { Interest } \times 100}{\text { Principal } \times \text { Rate }}\)
= \(\frac{100 \times 100}{100 \times \frac{25}{4}}=\frac{100 \times 4}{25}=16 \text { years }\)
∴ Required time = 16 years.
Question 2. The rate of simple interest per annum reduces by 4% to 3 3/4 %, and for this, Amal bab’s annual income decreases by s. 60, Let us determine Amal babu’s principal.
Solution: On Rs. 100, income (Interest) decreased from Rs 4 to Rs. \(3 \frac{3}{4}\)
= Rs \(4-3 \frac{3}{4}=\frac{1}{4}\) in 1 year
∴ His income decreases by Rs, \(\frac{1}{4}\) in 1 year on Rs. 100.
∴ His income decreases by Rs. 40 in 1 year an Rs. \(\frac{100}{1 / 4} \mathrm{n} 60\)
= Rs. 100 x 4 x 60 = Rs. 24000.
∴ Amal babu’s capital = Rs. 24000.
Question 3. What is the rate of simple interest per annum, when the interest of the same money for 4 yrs. will be 8/25 part of its principal – let us determine it.
Solution: Let the principal = Rs. x
∴ Interest = \(\text { PB. } \frac{B}{25} x\)
Time = 4 years
Rate = \(\frac{\text { Interest } \times 100}{\text { Principal } \times \text { Time }}=\frac{\frac{8}{25} \times \times \times 100}{x \times 4}=8\)
∴ Rate = 4%.
Question 4. What is the rate of simple interest per annum, when the interest of some money is in 10 yrs. will be 2/5 part of its amount (principal along with interea1) – Let us determine it.
Solution: Let the amount = Rs. x
∴ Interest = \(\frac{2}{5} \cdot \times \text { Rs. } x=\text { Rs. } \frac{2 x}{5}\)
∴ Principal = \(\text { Rs. }\left(x-\frac{2 x}{5}\right)={Rs} \cdot \frac{5 x-2 x}{5}={Rs} \cdot \frac{3 x}{5}\)
Time = 10 years
∴ Rate = \(\frac{\text { Interest } \times 100}{\text { Principal } \times \text { Time }}\)
= \(\frac{\frac{2 x}{5} \times 100}{\frac{3 x}{5} \times 10}\)
= \(\frac{20 \times 2}{2 \times 3}=\frac{20}{3}=6 \frac{2}{3}\)
∴ Rate = \(6 \frac{2}{3}\)
Question 5. Let us determine the money for which monthly interest is Re. 1 having the rate of simple interest of 5% per annum.
Solution: Here let principal = Rs. x.
Rate = 5%
Interest = Rs 1
∴ Principal = \(\frac{\text { Interest } \times 100}{\text { Rate } \times \text { Time }}\)
= \(\frac{1 \times 100}{5 \times \frac{1}{12}}\)
= Rs. 20 x 12
= 240