 # RD Sharma Solutions Class 7 Simple Interest Exercise 13.1

## RD Sharma Solutions Class 7 Chapter 13 Exercise 13.1

#### Exercise 13.1

Q 1. Find the simple interest, when:

(i) Principal = Rs. 2000, Rate of interest = 5% per annum and Time = 5 years

Solution: It is given that;

Principal (P) = Rs. 2000

Rate of interest (R) = 5% p.a.

Time (T) = 5 years

Now, Simple Interest (SI)= (P × R × T)/100 = (2000 × 5 × 5)/100 = Rs. 500

(ii) Principal = Rs. 500, Rate of interest = 12.5% per annum and Time = 4 years

Solution: P = Rs. 500

R = 12.5% p.a.

T = 4 years

SI = (P × R × T)/100 = (500 × 12.5 × 4)/100 = Rs. 250

(iii) Principal = Rs . 4500, Rate of interest = 4% per annum and Time = 6 months

Solution: P = Rs. 4500

R = 4% p.a.

T = 6 months

T = 6/12 = 0.5 year [Since, 1 Year = 12 Months]

SI = (P × R × T)/100 = (4500 × 4 × 0.5)/100 = Rs. 90

(iv) Principal =Rs . 12000, Rate of interest = 18% per annum and Time = 4 months

Solution: P = Rs. 12000

R = 18% p.a.

T = 4 months = 4/12 = 1/3 years [Since, 1 Year = 12 Months]

SI = (P × R × T)/100 = (12000 × 18 × 1/3)/100 = Rs. 720

(v) Principal = Rs . 1000, Rate of interest = 10% per annum and Time = 73 days

Solution: P = Rs. 1000

R = 10% p.a.

T = 73 days = 73/365 = 0.2 [Since, 1 Year = 365 Days]

SI = (P × R × T)/100 = (1000 × 10 × 0.2)/100 = Rs. 20

Q 2. Find the interest on Rs. 500 for a period of 4 years at the rate of 8% per annum. Also, find the amount to be paid at the end of the period.

Solution: It is given that,

P = Rs. 500, R = 8% p.a., T = 4 years

SI = (P × R × T)/100 = (500 × 8 × 4)/100 = Rs. 160

Total amount paid = Principal + Simple Interest = Rs 500 + 160 = Rs 660

Q 3. A sum of Rs. 400 is lent at the rate of 5% per annum. Find the interest at the end of 2 years.

Solution: It is given that,

P = Rs. 400

R = 5% p.a.

T = 2 years

Interest paid after 2 years,

SI = (P × R × T)/100 = (400 × 5 × 2)/100 = Rs. 40

Q 4. A sum of Rs. 400 is lent for 3 years at the rate of 6% per annum. Find the interest.

Solution: It is given that,

P = Rs. 400

R = 6% p.a.

T = 3 years

Simple Interest after 3 years;

SI = (P × R × T)/100 = (400 × 6 × 3)/100 = Rs. 72

Q 5. A person deposits Rs. 25000 in a firm who pays an interest at the rate of 20% per annum . Calculate the income he gets from it annually.

Solution: It is given that,

P = Rs. 25000

R = 20% p.a.

T = 1 year

Income that the person will get;

SI = (P × R × T)/100 = (25000 × 2 × 1)/100 = Rs. 5000

Q 6. A man borrowed Rs. 8000 from a bank at 8% per annum . Find the amount he has to pay after $4\frac{1}{2}$ years .

Solution: It is given that,

P = Rs 8000

R = 8% p.a.

T = $4\frac{1}{2}$ years = 9/2 = 4.5 years

SI = (P × R × T)/100 = (8000 × 8 × 4.5)/100 = Rs. 2880

Total amount paid after $4\frac{1}{2}$ years;

A = P + SI = 8000 + 2880 = Rs. 10880

Q 7. Rakesh lent out Rs. 8000 for 5 years at 15 % per annum and borrowed Rs. 6000 for 3 years at 12% per annum. How much did he gain or lose?

Solution: It is given that,

Interest on the amount lent by Rakesh;

P = Rs 8000, R = 15% p.a., T = 5 years

SI = (P × R × T)/100 = (8000 × 15 × 5)/100 = Rs. 6000

Interest on the amount borrowed by Rakesh;

P = Rs 6000, R = 12% p.a., T = 3 years

SI = (P × R × T)/100 = (6000 × 12 × 3)/100 = Rs. 2160

Amount gained by Rakesh = Interest Lent – Interest Borrowed

= 6000 – 2160 = Rs. 3840

Q 8. Anita deposits Rs. 1000 in a savings bank account. The bank pays interest at the rate of 5 % per annum. What amount can Anita get after 1 year?

Solution: It is given that,

P = Rs 1000, R = 5% p.a., T = 1 year

SI = (P × R × T)/100 = (1000 × 5 × 1)/100 = Rs. 50

Amount that Anita got after 1 year;

A = P + SI = 1000 + 50 = Rs. 1050

Q 9. Nalini borrowed Rs. 550 from her friend at 8% per annum. She returned the amount after six months. How much did she pay ?

Solution: It is given that,

P = Rs 550, R = 8% p.a.

T = 6 months = 6/12 = 0.5 year [Since, 1 Year = 12 Months]

SI = (P × R × T)/100 = (550 × 8 × 0.5)/100 = Rs. 22

Total amount paid after 6 months;

A = P + SI = 550 + 22 = Rs. 572

Q 10. Rohit borrowed Rs. 60000 from a bank at 9% per annum for 2 years. He lent this sum of money to Rohan at 10% per annum for 2 years. How much did Rohit earn from this transaction?

Solution: Interest on the amount borrowed by Rohit;

P = Rs. 60000, R = 9% p.a., T = 2 years

SI = (P × R × T)/100 = (60000 × 9 × 2)/100 = Rs. 10800

Interest on the money lent by Rohit;

P = Rs. 60000, R = 10% p.a., T = 2 years

SI = (P × R × T)/100 = (60000 × 10 × 2)/100 = Rs. 12000

Amount gained by Rohit = Interest on the money lent by Rohit – Interest on the amount borrowed by Rohit

= 12000 – 10800 = Rs. 1200

Q 11. Romesh borrowed Rs. 2000 at 2% per annum and Rs. 1000 at 5% per annum. He cleared his debt after 2 years by giving Rs. 2800 and a watch. What is the cost of watch?

Solution: It is given that

Amount borrowed by Romesh

P = Rs. 2000, R = 2% p.a., T = 2 years

SI = (P × R × T)/100 = (2000 × 2 × 2)/100 = Rs. 80

Amount, A = P + SI

A = 2000 + 80 = Rs. 2080

Again he borrowed the money at

P = Rs. 1000, R = 5% p.a., T = 2 years

SI = (P × R × T)/100 = (1000 × 5 × 2)/100 = Rs. 100

A = P + SI = 1000 + 100 = Rs. 1100

Total amount that Romesh have to return = 2080 + 1100 = Rs. 3180

Amount repaid = 2800 + Watch

3180 = 2800 + watch

watch = Rs. 380

Thus, the value of the watch is Rs. 380.

Q 12. Mr Garg lent Rs. 15000 to his friend. He charged 15% per annum on Rs. 12500 and 18% on the rest. How much interest does he earn in 3 years?

Solution: P = Rs 12500, R = 15% p.a., T = 3 years

SI = (P × R × T)/100 = (12500 × 15 × 3)/100 = Rs. 5625

Rest of the amount lent = 15000 – 12500 = Rs. 2500

P = Rs. 2500, R = 18 % p.a., T = 3 years

SI = (P × R × T)/100 = (2500 × 18 × 3)/100 = Rs. 1350

Total interest earned in 3 years = 5625 + 1350 = Rs. 6975

Q 13. Shikha deposited Rs. 2000 in a bank which pays 6% simple interest. She withdrew Rs. 700 at the end of first year. What will be her balance after 3 years?

Solution: Interest on amount deposited by Shikha

P = Rs. 2000, R = 6% p.a., T = 1 year

SI = (P × R × T)/100 = (2000 × 6 × 1)/100 = Rs. 120

Amount = Principal + Simple Interest = 2000 + 120 = Rs 2120

After 1 year, amount withdrawn = Rs 700

Amount left after 1 year (P1) = Rs 2120 – Rs 700 = Rs 1420

P1 = 2120, R = 6% p.a., T = 2 years

SI = (P × R × T)/100 = (2120 × 6 × 2)/100 = Rs. 170.40

Total amount after 3 years = Rs 1420 + Rs 170.40 = Rs 1590.40

Shikha balance after 3 years is Rs. 1590.40

Q 14. Reema took a loan of Rs. 8000 from a money lender, who charged interest at the rate of 18% per annum. After 2 years, Reema paid him Rs. 10400 and wrist watch to clear the debt. What is the price of the watch?

Solution: Reema took loan for 2 years.

P = Rs. 8000, R = 18%, T = 2 years

Interest after 2 years;

SI = (P × R × T)/100 = (8000 × 18 × 2)/100 = Rs. 2880

Total amount payable by Reema after 2 years = 8000 + 2880 = Rs. 10,880

But it is given that Rs. 10,400 and a wrist watch.

Amount paid by Reema = Rs 10400 + Wrist watch

10880 = 10400 + Wrist watch

Wrist watch = Rs. 480

Thus the value of the watch is Rs. 480.

Q 15. Mr Sharma deposited Rs. 20000 as a fixed deposit in a bank at 10% per annum. If 30% is deducted as income tax on the interest earned, find his annual income.

Solution: Interest earned by Mr Sharma after 1 year;

P = Rs 20000, R = 10% p.a., T = 1 year

SI = (P × R × T)/100 = (20000 × 10 × 1)/100 = Rs. 2000

Amount deducted as income tax = 30% of Rs 2,000 = (30/100) × 2000 = Rs. 600

Annual income after tax deduction = 2000 – 600 = Rs. 1400