Rd Sharma 2018 Solutions for Class 7 Math Chapter 13 Simple Interest are provided here with simple step-by-step explanations. These solutions for Simple Interest are extremely popular among Class 7 students for Math Simple Interest Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rd Sharma 2018 Book of Class 7 Math Chapter 13 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rd Sharma 2018 Solutions. All Rd Sharma 2018 Solutions for class Class 7 Math are prepared by experts and are 100% accurate.

Page No 13.7:

Question 1:

Find the simple interest, when:
(i) Principal = Rs 2000, Rate of Interest = 5% per annum and Time = 5 years.
(ii) Principal = Rs 500, Rate of Interest = 12.5% per annum and Time = 4 years.
(iii) Principal = Rs 4500, Rate of Interest = 4% per annum and Time =  months.
(iv) Principal = Rs 12000, Rate of Interest = 18% per annum and Time = 4 months.
(v) Principal = Rs 1000, Rate of Interest = 10% per annum and Time = 73 days.

Answer:

(i) Principal (P) = Rs 2000
Rate of interest (R) = 5% p.a.
Time (T) = 5 years
Simple interest =  P×R×T100=2000×5×5100=Rs 500

(ii)  Principal (P) = Rs 500
Rate of interest (R) = 12.5% p.a.
Time (T) = 4 years
Simple interest = P×R×T100=500×12.5×4100=Rs 250

(iii) Principal (P) = Rs 4500
Rate of interest (R) = 4% p.a.
Time (T) = 6 months 

T =612=12 year (1 year = 12 months)
Simple interest = P×R×T100=4500×4×12100=4500×4×1100×2=Rs 90

(iv) Principal (P) = Rs 12000
Rate of interest (R) = 18% p.a.
​Time (T) = 4 months =412=13year       (1 year = 12 months)

Simple interest = P×R×T100=12000×18×1100×3=Rs 720 

(v) Principal (P) = Rs 1000
Rate of interest (R) = 10% p.a.
Time (T) = 73 days = 73365 year   (1 year = 365 days)

Simple interest = P×R×T100=1000×10×73100×365=Rs 20



Page No 13.8:

Question 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.

Answer:

Principal amount (P) = Rs 500
Time period (T) = 4 years
Rate of interest (R)  = 8% p.a.

 Interest = P×R×T100=500×4×8100=Rs 160

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

Page No 13.8:

Question 3:

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

Answer:

Principal amount (P) = Rs 400
Time period (T) = 2 years
Rate of interest (R)  = 5% p.a.

Interest paid after 2 years=P×R×T100=400×5×2100=Rs 40

Page No 13.8:

Question 4:

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

Answer:

Principal amount (P) = Rs 400
Time period (T) = 3 years
Rate of interest (R)  = 6% p.a.
Interest after 3 years = P×R×T100=400×6×3100 = Rs 72

Page No 13.8:

Question 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.

Answer:

Principal amount (P) = Rs 25000
Time period (T) = 1 year
Rate of interest (R)  = 20% p.a.
Annual interest = P×R×T100=25000×20×1100 = Rs 5000

Page No 13.8:

Question 6:

A man borrowed Rs 8000 from a bank at 8% per annum. Find the amount he has to pay after 412 years.

Answer:

Principal amount (P) = Rs 8000
Time period (T) = 412=92 years
Rate of interest (R)  = 8% p.a.
Interest = P×R×T100=8000×8×9100×2 = Rs 2880

Total amount paid after 412 years  = Principal amount + Interest = Rs 8000 + Rs 2880
                                                                                                 = Rs 10880

Page No 13.8:

Question 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?

Answer:

Principal amount lent out by Rakesh (P) = Rs 8000
Time period (T) = 5 years
Rate of interest (R)  = 15% p.a.
Interest = P×R×T100=8000×15×5100 = Rs 6000

Principal amount borrowed by Rakesh (P) = Rs 6000
Time period (T) = 3 years
Rate of interest (R) = 12% p.a.
 Interest = P×R×T100=6000×12×3100 = Rs 2160

Amount gained by Rakesh = Rs 6000 − Rs 2160 = Rs 3840

Page No 13.8:

Question 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 one year?

Answer:

Principal amount (P) = Rs 1000
Time period (T) = 1 year
Rate of interest (R) = 5% p.a.

 Interest = P×R×T100=1000×5×1100 = Rs 50

Total amount paid after 1 year = Principal amount + Interest = Rs 1000 + Rs 50
                                                                                           = Rs 1050

Page No 13.8:

Question 9:

Nalini borrowed Rs 550 from her friend at 8% per annum. She returned the amount after 6 months. How much did she pay?

Answer:

Principal amount (P) = Rs 550
Time period (T)  = 6 months = 612=12 year        (1 year = 12 months)
Rate of interest (R)  = 8% p.a.

 Interest = P×R×T100=550×8×1100×2=Rs 22

Total amount paid after 6 months = Principal amount + Interest = Rs 550 + Rs 22
                                                                                               = Rs 572

Page No 13.8:

Question 10:

Rohit borowed Rs 600000 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?

Answer:

Principal amount lent out by Rohit (P) = Rs. 60000
Time period (T)        = 2 years
Rate of interest (R)  = 10% p.a.

 Interest = P×R×T100= Rs.60000×10×2100= Rs. 12000

Principal amount borrowed by Rohit from the bank (P) = Rs. 60000
Time period (T)                                         = 2 years
Rate of interest (R)                                   = 9% p.a.
 Interest = P×R×T100= Rs.60000×9×2100= Rs. 10800

Amount gained by Rohit = Rs. 12000 - 10800 = Rs. 1200

Page No 13.8:

Question 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 the watch?

Answer:

Principal amount borrowed by Romesh (P) = Rs. 2000
Time period (T)        = 2 years
Rate of interest (R)  = 2% p.a.

 Interest = P×R×T100= Rs.2000×2×2100= Rs.80

Principal amount borrowed by Romesh (P) = Rs. 1000
Time period (T)        = 2 years
Rate of interest (R)  = 5% p.a.

 Interest = P×R×T100=Rs.1000×5×2100= Rs.100

Total amount that he will have to return  = Rs. 2000 + 1000 + 80 + 100 = Rs. 3180

Amount repaid = Rs. 2800
Value of the watch = Rs. 3180 - 2800 = Rs. 380

Page No 13.8:

Question 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?

Answer:

Principal amount (P) = Rs 12500
Time period (T) = 3 years
Rate of interest (R)  = 15% p.a.

Interest = P×R×T100=12500×15×3100 = Rs 5625

Rest of the amount lent =  Rs 15000 − Rs 12500 = Rs 2500
Rate of interest = 18 % p.a.
Time period = 3 years

 Interest = P×R×T100=2500×18×3100 = Rs 1350

Total interest earned = Rs 5625 + Rs 1350 = Rs 6975

Page No 13.8:

Question 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?

Answer:

Principal amount deposited  (P) = Rs 2000
Time period (T) = 1 year
Rate of interest (R)  = 6% p.a.
Interest after 1 year = P×R×T100=2000×6×1100=Rs 120 
So amount after 1 year = Principal amount + Interest = 2000 + 120 = Rs 2120
After 1 year, amount withdrawn = Rs 700
Principal amount left (P1) = Rs 2120 − Rs 700 = Rs 1420
Time period (T) = 2 years
Rate of interest (R)  = 6% p.a.
 Interest after 2 years = P1×R×T100=1420×6×2100=Rs 170.40 

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

Page No 13.8:

Question 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?

Answer:

Principal amount (P) = Rs 8,000
Rate of interest (R) = 18%
Time period (T) = 2 years
Interest after 2 years = P×R×T100=8000×18×2100 = Rs 2,880
Total amount payable by Reema after 2 years = Rs 8,000 + Rs 2,880 = Rs 10,880
Amount paid = Rs 10,400
Value of the watch = Rs 10,880 − Rs 10,400 = Rs 480

Page No 13.8:

Question 15:

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

Answer:

Amount deposit (P) = Rs 20,000
Rate of interest (R) = 10% p.a.
Time period (T) = 1 year

Interest after 1 year = P×R×T100=20000×10×1100 = Rs 2,000

Amount deducted as income tax = 30% of Rs 2,000 =30×2000100=Rs 600

Annual interest after tax deduction = Rs 2,000 − Rs 600 = Rs 1,400

Page No 13.8:

Question 1:

If the simple interest on a certain sum for 2 years at the rate of 5% per annum is â‚¹4000, then the sum is

(a) â‚¹46,000
(b) â‚¹44,000
(c) â‚¹40,000
(d) â‚¹48,000

Answer:

We know, I=P×T×R100

It is given that,
T = 2 years
R = 5%
I = â‚¹4000

Then,
4000=P×5×21004000=10P100P=40000

Thus, P = â‚¹40,000

Hence, the correct option is (c).



Page No 13.9:

Question 2:

In how many years will a certain sum become 3 times itself at 25% per annum under simple interest?

(a) 5
(b) 8
(c) 12
(d) 6

Answer:

Amount = 3 times the sum = 3P

Simple interest (I) = Amount − Sum = 3P − P = 2P

Let the sum (P) be x.
Then, simple interest (I) = 2x
Rate (R) = 25%
Time = T

I=P×R×T100T=100×IP×R      =100×2xx×25      =4×2      =8 years

Hence, the correct option is (b).

Page No 13.9:

Question 3:

The amount on â‚¹25,000 at 8% per annum for 6 years under simple interest is

(a) â‚¹35,000
(b) â‚¹37,000
(c) â‚¹45,000
(d) â‚¹47,000

Answer:

It is given that,
Sum (P) = â‚¹25,000
Rate (R) = 8%
Time (T) = 6 years

I=P×R×T100 =25000×8×6100 =12000

Therefore, simple interest (I) = â‚¹12,000

Now, Amount = P + I = â‚¹25,000 + â‚¹12,000 = â‚¹37,000
 
Hence, the correct option is (b).

Page No 13.9:

Question 4:

The simple interest for â‚¹1500 at 8% per annum for 3 years is

(a) â‚¹400
(b) â‚¹360
(c) â‚¹450
(d) â‚¹500

Answer:

It is given that,
Sum (P) = â‚¹1500
Rate (R) = 8%
Time (T) = 3 years

I=P×R×T100 =1500×8×3100 =360

Therefore, simple interest (I) = â‚¹360
 
Hence, the correct option is (b).

Page No 13.9:

Question 5:

The difference between the interest obtained for â‚¹1000 at 12% per annum for 3 years and that for â‚¹1500 at 8% per annum for 112 years is

(a) â‚¹360
(b) â‚¹300
(c) â‚¹180
(d) â‚¹200

Answer:

It is given that,
Sum (P1) = â‚¹1000
Rate (R1) = 12%
Time (T1) = 3 years

I1=P1×R1×T1100   =1000×12×3100   =360                     ....(1)

Sum (P2) = â‚¹1500
Rate (R2) = 8%
Time (T2) = 112 years = 32 years

I2=P2×R2×T2100   =1500×8×3100×2   =180                     ....(2)

Subtracting (2) from (1), we get
I2-I1=360-180=180

Hence, the correct option is (c).

Page No 13.9:

Question 6:

Which of the following yields maximum interest for 2 years?

(a) â‚¹1500 at 8% per annum
(b) â‚¹1000 at 11% per annum
(c) â‚¹2000 at 5% per annum
(d) â‚¹900 at 20% per annum

Answer:

(a) It is given that,
Sum (P1) = â‚¹1500
Rate (R1) = 8%
Time (T1) = 2 years

I1=P1×R1×T1100   =1500×8×2100   =240                     ....(1)

(b) It is given that,
Sum (P2) = â‚¹1000
Rate (R2) = 11%
Time (T2) = 2 years

I2=P2×R2×T2100   =1000×11×2100   =220                     ....(2)

(c) It is given that,
Sum (P3) = â‚¹2000
Rate (R3) = 5%
Time (T3) = 2 years

I3=P3×R3×T3100   =2000×5×2100   =200                     ....(3)

(d) It is given that,
Sum (P4) = â‚¹900
Rate (R4) = 20%
Time (T4) = 2 years

I4=P4×R4×T4100   =900×20×2100   =360                     ....(4)

From (1), (2), (3) and (4),
₹900 at 20% per annum yields maximum interest for 2 years.
​
Hence, the correct option is (d).

Page No 13.9:

Question 7:

If a sum of â‚¹3000 is lent out at 3% per annum for 20 years under simple interest, then the amount at the end of 20th year is

(a) â‚¹1800
(b) â‚¹1080
(c) â‚¹3600
(d) â‚¹4800

Answer:

It is given that,
Sum (P) = â‚¹3000
Rate (R) = 3%
Time (T) = 20 years

I=P×R×T100   =3000×3×20100   =1800

Amount = I + P = â‚¹1800 + â‚¹3000 = â‚¹4800

Hence, the correct option is (d).

Page No 13.9:

Question 8:

If a sum of â‚¹2000 is lent out at 2% per annum for 10 years under simple interest, then the amount is

(a) â‚¹1400
(b) â‚¹2400
(c) â‚¹200
(d) â‚¹1500

Answer:

It is given that,
Sum (P) = â‚¹2000
Rate (R) = 2%
Time (T) = 10 years

I=P×R×T100   =2000×2×10100   =400

Amount = I + P = â‚¹400 + â‚¹2000 = â‚¹2400

Hence, the correct option is (b).

Page No 13.9:

Question 9:

If interest on â‚¹x for 2 years at R% per annum is â‚¹80, the interest on â‚¹2x for one year at R% per annum is

(a) â‚¹160
(b) â‚¹40
(c) â‚¹80
(d) â‚¹120

Answer:

It is given that,
Sum (P1) = â‚¹x
Rate (R1) = R%
Time (T1) = 2 years
Interest (I1) = â‚¹80

I1=P1×R1×T110080=x×R×2100        =2Rx100              ...(1)

Now,
Sum (P2) = â‚¹2x
Rate (R2) = R%
Time (T2) = 1 year

I2=P2×R2×T2100   =2x×R×1100   =2Rx100   =80              From 1

Therefore, I2 = â‚¹80

Hence, the correct option is (c).

Page No 13.9:

Question 10:

At simple interest a sum becomes 4940 of itself in 212 years. The rate of interest per annum is

(a) 7%
(b) 8%
(c) 12%
(d) 9%

Answer:

Amount = 4940 times the sum = 4940P

Simple interest (I) = Amount − Sum = 4940P − P = 940P

Let the sum (P) be x.
Then, simple interest (I) = 940x
Rate (R) = R%
Time (T) = 212 years = 52 years

I=P×R×T100R=100×IP×T      =100×940xx×52      =455      =9%

Hence, the correct option is (d).

Page No 13.9:

Question 11:

At what rate percent per annum simple interest will a sum double itself in 10 years?

(a) 8%
(b) 10%
(c) 12%
(d) 1212%

Answer:

Amount = 2 times the sum = 2P

Simple interest (I) = Amount − Sum = 2P − P = P

Let the sum (P) be x.
Then, simple interest (I) = x
Rate (R) = R%
Time (T) = 10 years

I=P×R×T100R=100×IP×T      =100×xx×10      =10%

Hence, the correct option is (b).

Page No 13.9:

Question 12:

In what time will a sum of â‚¹8000 amount to â‚¹8360 at 6% per annum simple interest?

(a) 8 months
(b) 9 months
(c) 114 months
(d) 112 years

Answer:

It is given that,
Amount = â‚¹8360
Sum = â‚¹8000

Simple interest (I) = Amount − Sum = â‚¹8360 − â‚¹8000 = â‚¹360

Also,
Rate (R) = 6%
Time (T) = T years

I=P×R×T100T=100×IP×R      =100×3608000×6      =34 years      =34×12 months      =9 months

Hence, the correct option is (b).

Page No 13.9:

Question 13:

If a, b and c are three sums of money such that b is the simple interest on a and c is the simple interest on b for the same time and same rate. Which of the following is correct?

(a) abc = 1
(b) c2 = ab
(c) b2 = ac
(d) a2 = bc

Answer:

It is given that,
Simple interest (I1) = b
Sum (P1) = a
Rate (R1) = R%
Time (T1) = T years

Now,
I1=P1×R1×T1100b=a×R×T100R×T=100ba              ....(1)

Also,
Simple interest (I2) = c
Sum (P2) = b
Rate (R2) = R%
Time (T2) = T years

Now,
I2=P2×R2×T2100c=b×R×T100R×T=100cb              ....(2)

On equating (1) and (2), we get
100ba=100cbb2=ac

Hence, the correct option is (c).

Page No 13.9:

Question 14:

The simple interest at R% per annum for n years will be â‚¹n on a sum of

(a) â‚¹n
(b) â‚¹100n
(c) â‚¹100n
(d) â‚¹100n2

Answer:

It is given that,
Simple interest (I) = ₹n
Rate (R) = R%
Time (T) = n years

I=P×R×T100P=100×IR×T      =100×nR×n      =100R

Hence, the correct option is (c).

Page No 13.9:

Question 15:

The simple interest on a certain sum is 1625 of the sum. If the rate percent per annum and the time are numerically equal, then the rate percent is

(a) 8%
(b) 4%
(c) 6%
(d) 12%

Answer:

Let the sum (P) be ₹x
Then, the simple interest (I) = ₹1625x

Also,
Rate (R) = R%
Time (T) = R years    (∵ the rate percent per annum and the time are numerically equal)

I=P×R×T100R=100×IP×TR=100×1625xx×RR×R=64xxR×R=8×8R=8%

Hence, the correct option is (a).

Page No 13.9:

Question 16:

At which rate percent per annum simple interest will a sum triple itself in 16 years?

(a) 12%
(b) 10.5%
(c) 11.5%
(d) 12.5%

Answer:

Amount = 3 times the sum = 3P

Simple interest (I) = Amount − Sum = 3P − P = 2P

Let the sum (P) be x.
Then, simple interest (I) = 2x
Rate (R) = R%
Time (T) = 16 years

I=P×R×T100R=100×IP×T      =100×2xx×16      =12.5%

Hence, the correct option is (d).



View NCERT Solutions for all chapters of Class 7