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Ganit Prakash - Class-X - Let us work out 2

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Q1 to Q10

Question 1

Two friends together took a loan of Rs. 15,000 from a bank to run a business at the rate of simple interest of 12% per annum. Let us write, by calculating, the interest they have to pay after 4yrs.

Given:

Principal ($P$) = Rs. 15000

Rate of Interest ($R$) = 12%

Time ($T$) = 4 yrs

We know, Interest ($I$) = $\frac{P\times R\times T}{100}$

$I=\frac{15000\times12\times4}{100}=150\times48=7200$

Answer: The interest they have to pay is Rs. 7200.

Question 2

Let us determine the interest on Rs. 2000 at the rate of simple interest of 6% per annum from 1st January to 27th May, 2005.

Given:

Principal ($P$) = Rs. 2000

Rate of Interest ($R$) = 6%

Time calculation from 1st Jan to 26th May (inclusive of 27th, exclusive of 1st):

Jan (30 days) + Feb (28 days) + Mar (31 days) + Apr (30 days) + May (27 days) = 146 days.

Time ($T$) = $\frac{146}{365}$ year = $\frac{2}{5}$ year

Interest ($I$) = $\frac{P\times R\times T}{100} = \frac{2000\times6\times2}{100\times5} = \frac{24000}{500} = 48$

Answer: The interest is Rs. 48.

Question 3

Let us determine the amount (Principal along with interest) on Rs. 960 at the rate of simple interest of $8\frac{1}{3}\%$ per annum for 1 yr. 3months.

Given:

Principal ($P$) = Rs. 960

Rate ($R$) = $8\frac{1}{3}\%=\frac{25}{3}\%$

Time ($T$) = 1 yr 3 months = $1\frac{3}{12}$ yrs = $1\frac{1}{4}$ yrs = $\frac{5}{4}$ yrs

Interest ($I$) = $\frac{P\times R\times T}{100} = \frac{960\times25\times5}{100\times3\times4} = \frac{960\times125}{1200} = 100$

Amount = Principal + Interest = $960+100=1060$

Answer: The amount is Rs. 1060.

Question 4

Utpalbabu took a loan of Rs. 3200 for 2yrs. from a Cooperative bank for cultivation of his land at the rate of simple interest of 6% per annum. Let us write by calculating, the amount he has to repay after 2yrs.

Principal ($P$) = Rs. 3200

Rate ($R$) = 6%

Time ($T$) = 2 yrs

Interest ($I$) = $\frac{P\times R\times T}{100} = \frac{3200\times6\times2}{100} = 384$

Amount = $P+I = 3200+384=3584$

Answer: He has to repay Rs. 3584.

Question 5

Sovadebi deposited a sum of money in a bank at the rate of simple interest of 5.25% per annum. After 2yrs. she has got Rs. 840 as interest. Let us write by calculating, the money she has deposited in the bank.

Given:

Interest ($I$) = Rs. 840

Rate ($R$) = 5.25%

Time ($T$) = 2 yrs

We know, Principal ($P$) = $\frac{100\times I}{R\times T}$

$P=\frac{100\times840}{5.25\times2}=\frac{84000}{10.5}=8000$

Answer: The money she deposited was Rs. 8000.

Question 6

Goutam took a loan from a Cooperative bank for opening a poultry farm at the rate of simple interest of 12% per annum. Every month he has to repay Rs. 378 as interest. Let us determine the loan amount taken by him.

Interest for 1 month ($I$) = Rs. 378

Rate ($R$) = 12%

Time ($T$) = 1 month = $\frac{1}{12}$ year

Principal ($P$) = $\frac{100\times I}{R\times T} = \frac{100\times378}{12\times\frac{1}{12}} = \frac{37800}{1} = 37800$

Answer: The loan amount is Rs. 37800.

Question 7

Let us calculate, period of time for which a sum of money becomes twice having the rate of simple interest of 6% per annum.

Let Principal be $P$.

Amount becomes twice, so Amount = $2P$.

Interest ($I$) = Amount - Principal = $2P-P=P$

Rate ($R$) = 6%

Time ($T$) = $\frac{100\times I}{P\times R} = \frac{100\times P}{P\times6} = \frac{100}{6} = \frac{50}{3} = 16\frac{2}{3}$ yrs

$\frac{2}{3}$ yrs = $\frac{2}{3}\times12=8$ months.

Answer: The time period is 16 years and 8 months.

Question 8

Mannan Miyan observed, after 6 years of taking a loan that the interest to be paid had become $\frac{3}{8}$th of its principal. Let us determine the rate of simple interest in percent per annum.

Let Principal be $P$.

Interest ($I$) = $\frac{3}{8}P$

Time ($T$) = 6 yrs

Rate ($R$) = $\frac{100\times I}{P\times T} = \frac{100\times\frac{3}{8}P}{P\times6} = \frac{100\times3}{8\times6} = \frac{300}{48} = \frac{25}{4} = 6.25\%$

Answer: The rate of simple interest is 6.25% (or $6\frac{1}{4}\%$).

Question 9

An agricultural Co-operative society gives agricultural loan to its members at the rate of simple interest of 4% per annum. But an interest is to be given at the rate of simple interest of 7.4% per annum for a loan taken from the bank. If a farmer being a member of the Co-operative society takes a loan of Rs. 5000 from it instead of taking loan from the bank, then let us write, by calculating the money to be saved as interest per annum.

Principal ($P$) = Rs. 5000

Time ($T$) = 1 yr

Difference in interest rates = $7.4\%-4\%=3.4\%$

Money saved = Interest calculated on the difference of rates

Saved amount = $\frac{P\times R_{diff}\times T}{100} = \frac{5000\times3.4\times1}{100} = 50\times3.4 = 170$

Answer: The money saved per annum is Rs. 170.

Question 10

If the interest of Rs. 292 in 1 day be 1 paisa, then let us write by calculating, the rate of simple interest in percent per annum.

Principal ($P$) = Rs. 292

Interest ($I$) = 1 paisa = Rs. 0.01

Time ($T$) = 1 day = $\frac{1}{365}$ yr

Rate ($R$) = $\frac{100\times I}{P\times T} = \frac{100\times0.01}{292\times\frac{1}{365}} = \frac{1}{\frac{292}{365}} = \frac{365}{292} = \frac{5}{4} = 1.25\%$

Answer: The rate of simple interest is 1.25% (or $1\frac{1}{4}\%$).

📗 Let us work out 2

Q11 to Q20

Question 11

Let us calculate the number of yrs. for which the interest on Rs. 600 at the rate of simple interest of 8% per annum will be Rs. 168.

Principal ($P$) = Rs. 600

Rate ($R$) = 8%

Interest ($I$) = Rs. 168

Time ($T$) = $\frac{100\times I}{P\times R} = \frac{100\times168}{600\times8} = \frac{168}{48} = 3.5$ yrs

Answer: The number of years is 3.5 years (or $3\frac{1}{2}$ years).

Question 12

If I get Rs. 1200 as amount (principal along with interest) by depositing Rs. 800 in the bank at the rate of simple interest of 10% per annum, then let us write by calculating, the time for which the money was deposited in the bank.

Amount ($A$) = Rs. 1200

Principal ($P$) = Rs. 800

Interest ($I$) = Amount - Principal = $1200-800=400$

Rate ($R$) = 10%

Time ($T$) = $\frac{100\times I}{P\times R} = \frac{100\times400}{800\times10} = \frac{40000}{8000} = 5$ yrs

Answer: The time is 5 years.

Question 13

At the same rate of simple interest per annum, if a principal yields the amount of Rs. 7100 in 7 yrs. and of Rs. 6200 in 4 yrs., let us determine the principal and rate of simple interest per annum.

Amount in 7 years = Principal + 7 years Interest = Rs. 7100

Amount in 4 years = Principal + 4 years Interest = Rs. 6200

Subtracting both: 3 years Interest = $7100-6200=900$

Interest for 1 year = $\frac{900}{3} = 300$

Interest for 4 years = $300\times4 = 1200$

Principal = Amount in 4 years - Interest for 4 years = $6200-1200=5000$

Rate ($R$) = $\frac{100\times I}{P\times T} = \frac{100\times300}{5000\times1} = \frac{30000}{5000} = 6\%$

Answer: Principal is Rs. 5000 and Rate is 6% per annum.

Question 14

Amal Roy deposits Rs. 2000 in a bank and Poshupoti Ghosh deposits Rs. 2000 in a post office at the same time. After 3yrs. they get the return amounts as Rs. 2360 and Rs. 2480 respectively. Let us write by calculating, the ratio of the rates of simple interest per annum in the bank and in the post office.

For Bank:

Principal = Rs. 2000, Amount = Rs. 2360, Time = 3 yrs

Interest = $2360-2000=360$

Rate ($R_{bank}$) = $\frac{100\times360}{2000\times3} = \frac{36000}{6000} = 6\%$

For Post Office:

Principal = Rs. 2000, Amount = Rs. 2480, Time = 3 yrs

Interest = $2480-2000=480$

Rate ($R_{post}$) = $\frac{100\times480}{2000\times3} = \frac{48000}{6000} = 8\%$

Ratio = $R_{bank} : R_{post} = 6 : 8 = 3 : 4$

Answer: The ratio is 3 : 4.

Question 15

A weaver Cooperative society takes a loan of Rs. 15,000 for buying a power loom. After 5 yr. the society has to repay Rs. 22125 for recovering the loan. Let us determine the rate of simple interest per annum.

Principal ($P$) = Rs. 15000

Amount ($A$) = Rs. 22125

Interest ($I$) = $22125-15000=7125$

Time ($T$) = 5 yrs

Rate ($R$) = $\frac{100\times I}{P\times T} = \frac{100\times7125}{15000\times5} = \frac{712500}{75000} = \frac{7125}{750} = 9.5\%$

Answer: The rate is 9.5% (or $9\frac{1}{2}\%$).

Question 16

Aslamchacha got Rs. 1,00,000 when he retired from his service. He deposited a part of that money in a bank and rest of his money in a post office and got Rs. 5400 in total per year as interest. If the rates of simple interest per annum in the bank and in the post office are 5% and 6%, respectively, then let us write by calculating, the sums of money he had deposited in the bank and post office.

Let the amount deposited in bank be Rs. $x$.

Then, amount deposited in post office = Rs. $(100000-x)$

Total interest for 1 year = Rs. 5400

$\frac{x\times5\times1}{100} + \frac{(100000-x)\times6\times1}{100} = 5400$

$\frac{5x + 600000 - 6x}{100} = 5400$

$600000 - x = 540000$

$x = 600000 - 540000 = 60000$

Bank deposit = Rs. 60000. Post office deposit = $100000-60000=40000$.

Answer: He deposited Rs. 60000 in the bank and Rs. 40000 in the post office.

Question 17

Rekhadidi deposited Rs. 10,000 of her savings in two separate banks at the same time. The rate of simple interest per annum is 6% in one bank and 7% in other bank; after 2 yr., if she gets Rs. 1280 in total as interest, then let us write by calculating, the sums of money she had deposited separately in each of the two banks.

Let deposit in first bank be Rs. $x$ and second bank be Rs. $(10000-x)$.

Interest from both banks for 2 years = Rs. 1280

$\frac{x\times6\times2}{100} + \frac{(10000-x)\times7\times2}{100} = 1280$

$\frac{12x + 140000 - 14x}{100} = 1280$

$140000 - 2x = 128000$

$2x = 140000 - 128000 = 12000 \implies x = 6000$

First bank deposit = Rs. 6000. Second bank deposit = $10000-6000=4000$.

Answer: She deposited Rs. 6000 and Rs. 4000 respectively.

Question 18

A bank gives 5% 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) that Dipubabu will get at the end of the year.

Rate ($R$) = 5%

First 3 months ($3/12$ yr): Principal = Rs. 15000

$I_1 = \frac{15000\times5\times3}{100\times12} = \frac{225000}{1200} = 187.5$

Next 3 months ($3/12$ yr): Principal = $15000-3000=12000$

$I_2 = \frac{12000\times5\times3}{100\times12} = \frac{180000}{1200} = 150$

Remaining 6 months ($6/12$ yr): Principal = $12000+8000=20000$

$I_3 = \frac{20000\times5\times6}{100\times12} = \frac{600000}{1200} = 500$

Total Interest = $187.5+150+500=837.5$

Final Principal at the end = Rs. 20000

Amount = Principal + Interest = $20000+837.5=20837.5$

Answer: The total amount is Rs. 20837.50.

Question 19

Rahamatchacha takes a loan of Rs. 2,40,000 from a bank for constructing a building at the rate of simple interest of 12% per annum. After 1yr. 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.

Let the total time taken to repay the loan be $x$ years.

Rent is started after 1 year, so rent duration = $(x-1)$ years.

Total rent collected = $5200\times12\times(x-1) = 62400(x-1)$

Total amount to repay = Principal + Interest = $240000 + \frac{240000\times12\times x}{100} = 240000 + 28800x$

Equating both:

$62400(x-1) = 240000 + 28800x$

$62400x - 62400 = 240000 + 28800x$

$62400x - 28800x = 240000 + 62400$

$33600x = 302400 \implies x = \frac{302400}{33600} = 9$

Answer: He would take 9 years to repay.

Question 20

Rothinbabu deposits money for each of his two daughters in such a way that when the ages of each of his daughters will be 18yrs. each one will get Rs. 1,20,000. The rate of simple interest per annum in the concerned bank is 10% and the present ages of his daughters are 13yr. and 8 yr. respectively. Let us determine the sums of money, he had deposited separately in the bank in favour of each of his daughters.

For Elder Daughter: Present age = 13. Time ($T$) = $18-13=5$ yrs.

Amount ($A$) = Rs. 120000. Rate = 10%.

Let Principal be $P_1$.

$P_1 + \frac{P_1\times10\times5}{100} = 120000 \implies P_1 + 0.5P_1 = 120000 \implies 1.5P_1 = 120000 \implies P_1 = 80000$

For Younger Daughter: Present age = 8. Time ($T$) = $18-8=10$ yrs.

Amount ($A$) = Rs. 120000. Rate = 10%.

Let Principal be $P_2$.

$P_2 + \frac{P_2\times10\times10}{100} = 120000 \implies P_2 + 1P_2 = 120000 \implies 2P_2 = 120000 \implies P_2 = 60000$

Answer: He deposited Rs. 80000 and Rs. 60000 respectively.

📗 Let us work out 2

Solutions: Q21 & Q22

Question 21 (A) (i) - M.C.Q

(i) If the interest of Rs. p at the rate of simple interest of r% per annum in t years is I, then
(a) I = prt   (b) prtI = 100   (c) prt = 100 $\times$ I   (d) none of these.

Formula: $I = \frac{prt}{100}$

$\implies 100 \times I = prt$

Answer: (c) $prt = 100 \times I$

Question 21 (A) (ii) - M.C.Q

(ii) A principal becomes twice as its amount in 20 yrs at a certain rate of simple interest. At the same rate of simple interest, that very principal becomes thrice as its amount in
(a) 30 yrs.   (b) 35 yrs.   (c) 40 yrs.   (d) 45 yrs.

Amount = 2P $\implies$ Interest = P in 20 yrs.

Amount = 3P $\implies$ Interest = 2P.

Time required for 2P interest = $2 \times 20 = 40$ yrs.

Answer: (c) 40 yrs.

Question 21 (A) (iii) - M.C.Q

(iii) If a principal becomes twice as its amount in 10 yrs., the rate of simple interest per annum is
(a) 5%   (b) 10%   (c) 15%   (d) 20%

Amount = 2P $\implies$ Interest = P.

Rate ($R$) = $\frac{100 \times P}{P \times 10} = 10\%$

Answer: (b) 10%

Question 21 (A) (iv) - M.C.Q

(iv) If the total interest comes upto Rs. x for a principal for the rate of simple interest of x% per annum in x years then the principal will be
(a) Rs. x   (b) Rs. 100x   (c) Rs. $\frac{100}{x}$   (d) Rs. $\frac{100}{x^2}$

$I = x$, $R = x\%$, $T = x$ yrs.

Principal ($P$) = $\frac{100 \times I}{R \times T} = \frac{100 \times x}{x \times x} = \frac{100}{x}$

Answer: (c) Rs. $\frac{100}{x}$

Question 21 (A) (v) - M.C.Q

(v) The total interest of a principal in n yrs. at the rate of simple interest of r% per annum is $\frac{pnr}{25}$, the principal will be
(a) Rs. 2p   (b) Rs. 4p   (c) Rs. $\frac{p}{2}$   (d) Rs. $\frac{p}{4}$

$I = \frac{pnr}{25}$, $T = n$ yrs, $R = r\%$.

Principal = $\frac{100 \times I}{R \times T} = \frac{100 \times \left(\frac{pnr}{25}\right)}{r \times n} = 4p$

Answer: (b) Rs. 4p

Question 21 (B) - True or False

(B) Let us write, whether the following statements are true or false:
(i) A man takes a loan is called debtor.
(ii) 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.

(i) True. A person who borrows money is in debt, hence called a debtor.

(ii) False. Interest ($I$) is directly proportional to Time ($T$) when Principal and Rate are constant ($I \propto T$).

Question 21 (C) - Fill in the blanks

(C) Let us fill in the blanks :
(i) A man who gives loan is called _____________.
(ii) The amount of Rs. 2p in t yr. at the rate of simple interest of $\frac{r}{2}\%$ per annum is Rs. (2p + __________).
(iii) 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 _________.

(i) creditor.

(ii) Interest = $\frac{2p \times (r/2) \times t}{100} = \frac{prt}{100}$. Amount = $2p + \frac{prt}{100}$. Blank: $\frac{prt}{100}$.

(iii) $P=8x$, $A=9x \implies I=1x$. Rate = $\frac{100 \times x}{8x \times 1} = 12.5\%$. Blank: 12.5.

Question 22 S.A. (i)

(i) Write the number of yrs. in which the amount becomes twice of the principal having the rate of simple interest $6\frac{1}{4}\%$ per annum.

Amount = 2P $\implies$ Interest ($I$) = P.

Rate ($R$) = $6\frac{1}{4}\% = \frac{25}{4}\%$

Time ($T$) = $\frac{100 \times P}{P \times (25/4)} = \frac{400}{25} = 16$

Answer: 16 years.

Question 22 S.A. (ii)

(ii) The rate of simple interest per annum reduces to $3\frac{3}{4}\%$ from 4% and for this, Amal babu's annual income decreases by Rs. 60. Let us determine Amal babu's principal.

Difference in Rate = $4\% - 3.75\% = 0.25\%$

Difference in Interest = Rs. 60, Time = 1 year.

Principal = $\frac{100 \times 60}{0.25 \times 1} = \frac{6000}{0.25} = 24000$

Answer: Rs. 24000.

Question 22 S.A. (iii)

(iii) What is the rate of simple interest per annum, when the interest of a principal in 4 yrs. will be $\frac{8}{25}$ part of its principal – let us determine it.

Interest ($I$) = $\frac{8P}{25}$, Time ($T$) = 4 yrs.

Rate ($R$) = $\frac{100 \times \left(\frac{8P}{25}\right)}{P \times 4} = \frac{32}{4} = 8\%$

Answer: 8%

Question 22 S.A. (iv)

(iv) What is the rate of simple interest per annum, when the interest of a sum of money in 10 yrs. will be $\frac{2}{5}$ part of its amount (principal along with interest) – Let us determine it.

$I = \frac{2}{5}A \implies 5I = 2(P + I) \implies 3I = 2P \implies I = \frac{2P}{3}$

Time ($T$) = 10 yrs.

Rate ($R$) = $\frac{100 \times \left(\frac{2P}{3}\right)}{P \times 10} = \frac{200}{30} = 6\frac{2}{3}\%$

Answer: $6\frac{2}{3}\%$

Question 22 S.A. (v)

(v) Calculate the principal whose monthly interest is Rs. 1 having the rate of simple interest of 5% per annum.

Interest ($I$) = Rs. 1

Time ($T$) = 1 month = $\frac{1}{12}$ year

Rate ($R$) = 5%

Principal = $\frac{100 \times 1}{5 \times (1/12)} = \frac{1200}{5} = 240$

Answer: Rs. 240.

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WBBSE Board — Class 10 Simple Interest - Ganit Prakash - Let us work out 2 Solutions.

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