## 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 Ã— R Ã— T)/100 = (2000 Ã— 5 Ã— 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 Ã— R Ã— T)/100 = (500 Ã— 12.5 Ã— 4)/100 = Rs. 250

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

**Solution:** P = Rs. 4500

R = 4% p.a.

T = 6 months

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

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

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

**Solution:Â **P = Rs. 12000

R = 18% p.a.

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

SI = (P Ã— R Ã— T)/100 = (12000 Ã— 18 Ã— 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 = 0.2Â [Since, 1 Year = 365 Days]

SI = (P Ã— R Ã— T)/100 = (1000 Ã— 10 Ã— 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 Ã— R Ã— T)/100 = (500 Ã— 8 Ã— 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 Ã— R Ã— T)/100 = (400 Ã— 5 Ã— 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 Ã— R Ã— T)/100 = (400 Ã— 6 Ã— 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 Ã— R Ã— T)/100 = (25000 Ã— 2 Ã— 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 = \(4\frac{1}{2}\)Â years = 9/2 = 4.5 years

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

Total amount paid afterÂ \(4\frac{1}{2}\)Â 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.,Â T = 5 years

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

Interest on the amount borrowed by Rakesh;

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

SI = (P Ã— R Ã— T)/100 = (6000 Ã— 12 Ã— 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 Ã— R Ã— T)/100 = (1000 Ã— 5 Ã— 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,Â R = 8% p.a.

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

SI = (P Ã— R Ã— T)/100 = (550 Ã— 8 Ã— 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:Â **Interest on the amount borrowed by Rohit;

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

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

Interest on the money lent by Rohit;

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

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

Amount gained by Rohit =Â Interest on the money lent by Rohit –Â 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,Â R = 2% p.a.,Â T = 2 years

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

Amount, A = P + SI

A = 2000 + 80 = Rs. 2080

Again he borrowed the money at

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

SI = (P Ã— R Ã— T)/100 = (1000 Ã— 5 Ã— 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:Â **P = Rs 12500, R = 15% p.a., T = 3 years

SI = (P Ã— R Ã— T)/100 = (12500 Ã— 15 Ã— 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 Ã— R Ã— T)/100 = (2500 Ã— 18 Ã— 3)/100 = Rs. 1350

Total interest earned in 3 yearsÂ = 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?Â **

**Solution: **Interest on amount deposited by Shikha

P = Rs. 2000,Â R = 6% p.a., T = 1 year

SI = (P Ã— R Ã— T)/100 = (2000 Ã— 6 Ã— 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 =Â 6% p.a.,Â T = 2 years

SI = (P Ã— R Ã— T)/100 = (2120 Ã— 6 Ã— 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,Â R = 18%, TÂ = 2 years

Interest after 2 years;

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

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

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

Amount paid by Reema = Rs 10400 + Wrist watch

10880 =Â 10400 + Wrist watch

Wrist watch =Â 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 Ã— R Ã— T)/100 = (20000 Ã— 10 Ã— 1)/100 = Rs. 2000

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

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