Question 1

Ramesh invested an amount that is 10% of ₹ 10000 at simple interest. After 3 yr, the amount becomes ₹ 2500. Find out the 4 times of actual interest rate.

Accepted Answer

Investment of Ramesh = 10% of 10000 = ₹ 1000 After 3 yr = 2500 - 1000 = ₹ 1500 We know. SI = (P x R x T)/100 ⇒ 1500 = (1000 x R x 3)/100 ∴ R = (1500 x 100) / (1000 x 3) = 50% ∴ 4 times of 50% = 200%

Question 2

What will be the ratio of simple interest earned by certain amount at the same rate of interest for 12 yr and for 18 yr?

Accepted Answer

If the principal = P and interest = R% Then, required ratio = [(P x R x 12)/100] / [(P x R x 18)/100] = 12 / 18 = 2/3 = 2 : 3

Question 3

A sum of Rs . 2600 is lent out in two part in such a way that the interest on one part at 10% for 5 years is equal to that on another part at 9% for 6 years. The sum lent out at 10% is?

Accepted Answer

Let the money at 10% be Rs. P, Then the money at 9% is Rs. (2600 - P ) ∴ (P x 10 x 5)/100 = [(2600 - P ) x 9 x 6]/100 or 104 x P = 2600 x 54 or P = (2600 x 54) / 104 = Rs.1350

Question 4

Simple interest on a certain sum at a certain rate is 9/16 of the sum. If the number representing rate percent and time in years be equal. Then the time is?

Accepted Answer

Let principle = P, then SI = (9/16) x P. Let rate = R% per annum and time = R years Then, 9/16 P = P x R x R / 100 ⇒ R2 = 900/16 ∴ R = 30/4 = 71/2 years

Question 5

The rate of interest on a sum of money is 4% per annum for the first 2 year, 6% per annum for the next 4 year and 8% per annum for the period beyond 6 years. If the simple interest accrued by the sum for a total period of 9 years is Rs. 1120. What i…

Accepted Answer

Let sum= Rs. P Then, [(P x 4 x 2) /100] + [(P x 6 x 4) / 100] + [(P x 8 x 3) /100] = 1120 ⇒ 56 x P = 112000 ∴ P = 112000/56 = Rs. 2000

Question 6

If A is the simple interest on B and B is the simple interest on C, the rate % and and the time being the same in both cases, what is the relation between A, B and C?

Accepted Answer

∵ A = (B x R x T) / 100 ....(i) And B = (C x R x T) / 100 ...(ii) From Eq. (i) and (ii) ⇒ A/B = B/C ∴ B2 = AC

Question 7

The rate of interest for the first 2 years is 5% for the next 3 years is 8% and beyond this. It is 10% per annum. If the simple interest for 8 years is Rs . 1280. What is the principal?

Accepted Answer

r1 = 5%, r2 = 8%, r3 = 10%, t1 = 2 years t2 = 3 years, t3 = 8 - (2 + 3) = 3 years ∵ Principal = (Interest x 100) / [(r1 x t1) + (r2 x t2) + (r3 x t3 )] = (1280 x 100) / (5 x 2 + 8 x 3 + 10 x 3) = 128000/(10 + 24 + 30) = 128000/64 =Rs. 2000

Question 8

Anil borrowed some money at simple interest. The rate of interest for the first 3 years was 5% for the next 2 years was 8% and for the next 4 year it was 10%. Beyond this it was 12% per annum. If he paid Rs. 8560, as interest for 12 years. How much …

Accepted Answer

r1 = 5% r2 = 8% r3 = 10% r4 = 12% t1 = 3 years t2 = 2 years t3 = 4 years t4 = 12 - (3 + 2 + 4) = 3 years ∵ Principal = ( Interest x 100) / ( r1 t1 + r2 t2 + r3 t3 + r4 t4) = (8560 x 100) / (5 x 3 + 8 x 2 + 10 x 4 + 12 x 3) = 856000/107 = Rs. 8000

Question 9

Prabhat borrowed some money from a bank at 8% p.a simple interest and lended it to Ashish at 12% p.a simple interest. If his profit in 2 years is Rs. 320. What sum of money did he borrow?

Accepted Answer

Let the principal be Rs. P ∴ Amount = Rs. 10080 ∴ Simple interest = Amount - Principal = 10080 - P &because Simple interest = (Principal x Rate x Time) / 100 ⇒ 10080 - P = (P x 16 x 5) / 100 ⇒ 10080 - P = 4P/5 ⇒ 50400 - 5P = 4P ⇒ 50400 = 5P + 4P ⇒ 50400 = 9P ∴ P = 50400/9 = Rs. 5600

Question 10

Pratap borrowed some money from Arun at simple interest. The rate of interest for the first 3 years was 12% for the next 5 years was 16% and beyond this it was 20%. If the simple interest for 11 years was more than the money borrowed by Rs. 6080. Wh…

Accepted Answer

Let the sum be P. SI = SI for first 3 years + SI for next 5 years + SI for next 3 years ⇒ P + 6080 = (P x 12 x 3) / 100 + (P x 16 x 5) / 100 + (P x 20 x 3) / 100 ⇒ P + 6080 = (36P + 80P + 60P) / 100 ⇒ 100 x (P + 6080) = 176P ∴ P = 608000 / 76 = 8000

Question 11

A sum ₹ 1440 is lent out in three parts in such a way that the interest on first part at 2% for 3 yr, second part at 3% for 4 yr and third part at 4% for 5 yr equal . Then, the difference between the largest and the smallest sum is?

Accepted Answer

Let the first part be ₹ A. second part be ₹ B and third part be Rs C According to the question. (A x 2 x 3)/100 = (B x 3 x 4)/100 = (C x 4 x 5)/ 100 ⇒ 3A = 6B = 10C = k ∴ A = k/3, B = k/100 and C = k /10 Now, A + B + C = 1440 ⇒ k/3 + k/6 + k/10 = 1440 ⇒ k = 2400 ∴ so the difference = k/3 - k/10 = 7k/30 = 7/30 x 2400 = ₹ 560

Question 12

Out of a certain sum, 1/3rd is invested at 3%, 1/6th at 6% and the rest at 8%. It the simple interest for 2 yr from all these investments amounts to ₹ 600 , find the original sum.?

Accepted Answer

Rest part = 1 - (1/3 + 1/6) = 1/2 Average rate per cent annum on the total sum = [(1/3) x 3] + [(1/6) x 6] + [(1/2) x 8] = 6% ∴ P = (100 x SI)/(R x T) = (100 x 600)/(6 x 2) = ₹ 5000

Question 13

A man buys a music system valued at ₹ 8000. He pays ₹ 3500 at once and rest 18 months later, on which he is charged simple interest at the rate of 8% per annum . Find the total amount he pays for the music system?

Accepted Answer

Cost of the music system = ₹ 8000 Money paid at once = ₹ 3500 Money left = (8000 - 3500) = ₹ 4500 Time = (18/12) = 3/2 yr and R = 8% per annum SI = PTR/100 = (4500 x 3/2 x 8)/100 = ₹ 540 Money to be paid at the end = (4500 + 540) = ₹ 5040 ∴ Cost of music system = (3500 + 5040) = ₹ 8540

Question 14

A man invests a certain sum of money at 6% per annum simple interest and another at 7% per annum simple interest. His income from interest after 2 yr was ₹ 792. Also, half of the first sum is equal to one-third of the second sum. The total sum inves…

Accepted Answer

Let the sum be P and Q, respectively. Then, (P x 6 x 2)/100 + (Q x 7 x 2)/100 = 792 ⇒ 6P + 7Q = 39600 ...(i) Also P/2 = Q/3 ⇒ 3P = 2Q ... (ii) On solving Eqs . (i) and (ii), we get P = 2400 and Q = 3600 ∴ Total sum = (2400 + 3600) = ₹ 6000

Question 15

A borrowed ₹ 4800 from B at 9% per annum simple interest for 3 yr. He, then added some more money to the borrowed sum and lent it to C for the same period at 12% per annum simple interest. If A gains ₹ 720 in the whole transaction, how much money di…

Accepted Answer

Let the money added be ₹ P, Then, [(4800 + P) x 12 x 3]/100 - (4800 x 9 x 3)/100 = 720 ⇒ (4800 + P) x 36 - (4800 x 27) = 720 x 100 ⇒ (4800 + P) x 4 - (4800 x 3) = 8000 ⇒ 4800 + P - (1200 x 3 ) = 2000 ⇒ P + 1200 = 2000 ∴ P = 800 So, money added is ₹ 800.

Question 16

A person closer his account in an investment scheme by withdrawing ₹ 10000. One year ago, he had withdraw ₹ 6000. Two years ago, he had withdrawn ₹ 5000. Three years ago, he had not withdrawn any money. How much money had he deposited approximately …

Accepted Answer

Suppose the person had deposited ₹ P at the time of opening the account . ∴ After one year he had P + (P x 10 x 1)/100 = ₹ 11P/10 After two years, he had 11P/10 + (11P/10 x 10 x 1)/100 = ₹ 121P/100 ...(i) After withdrawn ₹ 5000 from ₹ 121P/100, the balance = ₹ (121P - 500000)/100 After 3 yr, he had (121P - 500000)/100 + [(121P - 500000)/100 x 10 x 1]/100 = 11(121P - 500000)/100 ... (ii) After withdrawn ₹ 6000 from amount (ii) the balance = (1331P/1000 - 11500) ∴ After 4 yr, he had ₹ (1331P - 5500000)/1000 + 10% of ₹ (1331P - 5500000)/1000 = ₹ (11/10) x (1331P/1000 - 11500) ... (iii) After withdrawn ₹ 10000 from amount (iii) the balance =0 ∴ 11/10(1331P/1000 - 11500) - 10000 = 0 ⇒ P = ₹ 15470

Question 17

A certain sum becomes ₹ 600 in a certain time at the rate of 6% simple interest. The same sum amounts to ₹ 200 at the rate of 1% simple interest in the same duration. Find the sum and time.

Accepted Answer

According to the question. ([P + (P x 6 x T)/100] - [P + (P x 1 x T)/100] = 600 - 200 ⇒ 5PT/100 = 400 ⇒ PT = 8000 Again, for 6% rate, SI = PTR/100 = (8000 x 6)/100 = ₹ 480 ∴ Sum = 600 - 480 = ₹ 120 As we have, PT = 8000 ∴ T = 8000/120 = 200/3 = 662/3 yr

Question 18

The simple interest on a certain sum of money for 2 1/ 2 yr at 12% per annum is ₹ 20 less than the simple interest on the same sum for 3 1/ 2 yr at 10% per annum. Find the sum.

Accepted Answer

Given, T1 = 5/2, R1= 12% T2= 7/2 yr and R2 = 10% Let the sum be P. Then, [(P x 10 x 7)/(100 x 2)] - [(P x 12 x 5)/(100 x 2)] = 20 ⇒ (7P/20) - (3P/10) = 20 ∴ P = 20 x 20 = ₹ 400

Question 19

A sum was lent out for a certain time. The sum amounts to ₹ 400 at 10% annual interest rate. When the sum was lent out at 4% annual interest rate,it amounts to ₹ 200. Find the sum.

Accepted Answer

According to the question, [P + (P x R x T)/100] - [P + (P x 4 x T)/100] = 400 - 200 ⇒ (6 x PT) / 100 = 200 ⇒ PT = (200 x 100)/6 = 10000/3 Again, for 10% rate, SI= (P x 10 x T)/100 = (10000/3) x (10/100) = 1000/3 ∴ Sum(P) = 400 - (1000/3) = (1200 - 1000/3 = ₹ 200/3

Question 20

The annual payment of ₹ 160 in 5 yr at 5 % per annum simple interest will discharge a debt of

Accepted Answer

Given, annual payment = ₹ 160 R = 5% T = 5 yr debt (p) = ? According to the formula. Annual payment = 100P / [100 x T + {RT (T - 1)/2}] ⇒160 = 100P / [5 x 100 + {(5 x 4 x 5)/2}] ⇒ 160 = 100P/550 ∴ P = (550 x 160) / 100 = 55 x 16 = ₹ 880

Simple Interest Questions