All questions of Simple and Compound Interest for Electrical Engineering (EE) Exam

A father left a will of Rs.5 lakhs between his two daughters aged 10 and 15 such that they may get equal amounts when each of them reach the age of 21 years. The original amount of Rs.5 lakhs has been instructed to be invested at 10% p.a. simple interest. How much did the elder daughter get at the time of the will?
  • a)
    Rs.2,04,797
  • b)
    Rs.3,05,890
  • c)
    Rs.1,90,00
  • d)
    Rs.4,00,700
  • e)
    Rs.2,46,870
Correct answer is option 'A'. Can you explain this answer?

Akash Pandey answered
Answer – A.Rs.2,04,797 Explanation : Let Rs.x be the amount that the elder daughter got at the time of the will. Therefore, the younger daughter got (5,00,000 – x).
The elder daughter’s money earns interest for (21 – 15) = 6 years @ 10% p.a simple interest The younger daughter’s money earns interest for (21 – 10) = 11 years @ 10% p.a simple interest.
As the sum of money that each of the daughters get when they are 21 is the same, x + (6*10*x/100)= (5,00,000 – x) +(11*10*[5,00,000-x]/100) 100x+60x = (5,00,000-x)+(55,000,000-110x) 160x =55,500,000-111x 271x = 55,500,000 X = 2,04,797

Raghu lends Rs 50,000 of two of his friends. He gives Rs 30,000 to the first at 6% p.a. simple interest. He wants to make a profit of 10% on the whole. The simple interest rate at which he should lend the remaining sum of money to the second friend is
  • a)
    8%
  • b)
    16%
  • c)
    11%
  • d)
    17%
  • e)
    19%
Correct answer is option 'B'. Can you explain this answer?

Answer –B.16% Explanation : S.I. on Rs 30000 =(30000×6×1)/100 = Rs. 1800 Profit to made on Rs 50000 = 50000×10/100=Rs 5000 S.I.on Rs.20000 = 5000-1800 = Rs.3200 Rate=(S.I.* 100)/(P * T)=(3200×100)/20000 =16% per annum
Shortcut: 6……………………x ………..10…………….
3………………………2
4/(x-10)=2/3 x=16

Arun divides Rs 4702 among A, B, and C, so that if the amounts being invested at 4% simple interest, the amounts received after 2, 3 and 4 yrs by A, B, and C respectively is equal. Find the share of B?
  • a)
    Rs 1,458
  • b)
    Rs 1,556
  • c)
    Rs 2,358
  • d)
    Rs 1,237
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Anaya Patel answered
B) Rs 1,556 Explanation: 4702 will be divided in ratio – 1/[100+rt1] : 1/[100+rt2] : 1/[100+rt3] 1/[100+4*2] : 1/[100+4*3] : 1/[100+4*4] 1/108 : 1/112 : 1/116
= 812 : 783 : 756
So B gets 783/(812+783+756) * 4702 = 1566

Suresh lends 40% of his money at 15% per annum, 50% of the rest at 10% per annum and the rest at 18% per annum rate of interest. What would be the annual rate of interest, if the interest is calculated on the whole sum?
  • a)
    18.5%
  • b)
    14.4%
  • c)
    16.5%
  • d)
    19.5%
  • e)
    None of the Above
Correct answer is option 'B'. Can you explain this answer?

Preeti Khanna answered
B. 14.4%
Explanation: x – (40/100)*x = 60x/100 40/100 at 15% p.a = 40/100 * 15/100 = 60x/1000 50/100*60x/100 = 30x/100 at 10% p.a = 30x/100 * 10/100 = 30x/1000 Balance amount = x – 40x/100 – 30x/100 = 30x/100 at 18% p.a = 18/100 * 30x/100 = 54x/1000 R = [(144x/1000)/x] * 100 = 14.4%

A man borrows 10000 rupees at 20 % compound interest for 3 years. If every year he pays 2000 rupees as repayment. How much amount is still left to be paid by the man?
  • a)
    5000
  • b)
    7000
  • c)
    9000
  • d)
    10000
  • e)
    None of these
Correct answer is option 'D'. Can you explain this answer?

Aisha Gupta answered
Amount to be paid at the end of three years = 10000*(1+20/100)3 = 17280
Amount paid as instalment by the man = 2000*(1+20/100)2 + 2000*(1+20/100) + 2000 = 7280
So remaining amount = 10000

 A certain sum of money at certain rate of interest becomes Rs 3420 after 2 years and at same rate after two and a half years becomes Rs 3525. Find the rate percent per annum.
  • a)
    8.5%
  • b)
    8%
  • c)
    7%
  • d)
    10%
  • e)
    11%
Correct answer is option 'C'. Can you explain this answer?

Aarav Sharma answered
C) 7%
Explanation: Amount after 2.5 yrs = 3525, after 2 yrs = 3420 So SI for half yr = 3525-3420 = 105, so for 1 yr SI = 105*2 = 210 P + 2*SI = 3420
So P = 3420 – 2*210 = 3000 So 3000*r*2/100 = 420

A man borrows Rs 4000 at 8% compound interest for 3 years. At the end of each year he paid Rs 500. How much amount should he pay at the end of 3rd year to clear the debt?
  • a)
    Rs 4254.5
  • b)
    Rs 3465.2
  • c)
    Rs 3485.2
  • d)
    Rs 4345.4
  • e)
    Rs 3915.6
Correct answer is option 'E'. Can you explain this answer?

Anaya Patel answered
Amount after 1 yr = 4000[1 + 8/100] = 4320
Paid 500, so P = 4320 – 500 = 3820
Amount after 2nd yr = 3820[1 + 8/100] = 4125.6
So P= 4125.6-500 = 3625.6
Amount after 3rd yr = 3625.6[1 + 8/100] = 3915.6

Mohan invested 20000 rupee in fixed deposit at the rate of 10% simple interest.After every 3 rd year he added interest to principal. Find the interest earned at the end of 6 year.
  • a)
    7800
  • b)
    8000
  • c)
    7600
  • d)
    8200.
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Ravi Singh answered
Answer – a) 7800 Explanation : For the first 3 years SI will be = 20000*10/100*3 = 6000 Now he add 3000 to the principal i.e = 20000+6000 = 26000 Now interest earned at end of 6 year = 26000*10/100*3 = 7800

Riya saves an amount of 500 every year and then lent that amount at an interest of 10 percent compounded annually. Find the amount after 3 years.
  • a)
    1820.5
  • b)
    1840.5
  • c)
    1920.5
  • d)
    1940.5
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Aarav Sharma answered
Given:
Riya saves an amount of $500 every year.
Interest rate = 10% compounded annually.

To find:
The amount after 3 years.

Solution:
We can solve this problem using the compound interest formula:

A = P(1 + r/n)^(nt)

Where:
A = Final amount
P = Principal amount (initial savings)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years

Step 1: Calculate the final amount after 1 year.
P = $500
r = 10% = 0.10
n = 1 (compounded annually)
t = 1 year

A = 500(1 + 0.10/1)^(1*1)
A = 500(1 + 0.10)^1
A = 500(1.10)
A = $550

Step 2: Calculate the final amount after 2 years.
P = $550 (the amount after 1 year)
r = 10% = 0.10
n = 1 (compounded annually)
t = 2 years

A = 550(1 + 0.10/1)^(1*2)
A = 550(1 + 0.10)^2
A = 550(1.10)^2
A = 550(1.21)
A = $665.50

Step 3: Calculate the final amount after 3 years.
P = $665.50 (the amount after 2 years)
r = 10% = 0.10
n = 1 (compounded annually)
t = 3 years

A = 665.50(1 + 0.10/1)^(1*3)
A = 665.50(1 + 0.10)^3
A = 665.50(1.10)^3
A ≈ 665.50(1.331)
A ≈ $885.71

Therefore, the amount after 3 years is approximately $885.71.

Answer:
The correct answer is option A, 1820.5 (as given in the question). However, this answer is incorrect based on the calculations provided above.

A sum of rupees 4420 is to be divided between rakesh and prakash in such a way that after 5 years and 7 years respectively the amount they get is equal. The rate of interest is 10 percent. Find the share of rakesh and prakash
  • a)
    2000, 2420
  • b)
    2420, 2000
  • c)
    2480, 2420
  • d)
    2210, 2210
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
Given: Total amount = Rs. 4420, Rate of interest = 10%, Time for Rakesh = 5 years, Time for Prakash = 7 years

Let the share of Rakesh be x. Then, the share of Prakash will be (4420 - x).

Amount received by Rakesh after 5 years = x(1 + 10/100)^5 = 1.61x
Amount received by Prakash after 7 years = (4420 - x)(1 + 10/100)^7 = 1.97(4420 - x)

As per the question, both amounts should be equal. So, we can write:

1.61x = 1.97(4420 - x)
1.61x = 8717.4 - 1.97x
3.58x = 8717.4
x = 2420

Therefore, the share of Rakesh is Rs. 2420 and the share of Prakash is Rs. (4420 - 2420) = Rs. 2000.

Hence, option B is the correct answer.

If Rs. 7200 amounts to Rs.10368 at compound interest in a certain time , then Rs. 7200 amounts to what in half of the time?
  • a)
    8640
  • b)
    8600
  • c)
    8800
  • d)
    8520
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Ravi Singh answered
Let rate = R% and time = n year
Then, 10368 =7200(1+R/100)n
⇒ (1+R/100)n = 10368/7200 = 1.44
∴ (1 + R/100)n/2 = √1.44 = 1.2
∴ Required amount for n/2 yr
= 7200(1+ R/100)n/2
= 7200 x 1.2 = Rs. 8640

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