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Can you explain the answer of this question below:
A sum of money amounts to Rs.9800 after 5 years and Rs.12005 after 8 years at the same rate of simple interest. The rate of interest per annum is
  • A:15%
  • B:12%
  • C:8%
  • D:5%

The answer is B.

Arya Roy answered
We can get SI of 3 years = 12005 - 9800 = 2205

SI for 5 years = (2205/3)*5 = 3675 [so that we can get principal amount after deducting SI]

Principal = 12005 - 3675 = 6125 

So Rate = (100*3675)/(6125*5) = 12%

A sum of money placed at compound interest doubles itself in 4 years. In how many years will it amount to 8 times?
  • a)
    15
  • b)
    10
  • c)
    20
  • d)
    12
Correct answer is option 'B'. Can you explain this answer?

Aditya Kumar answered
Let,
Principal = Rs. 100.
Amount = Rs. 200.
Rate = r%
Time = 4 years.
Now,
A = P*[1+ (r/100)]n;
200 = 100*[1+(r/100)]4;
2 = [1+(r/100)]4; . (i)
If sum become 8 times in the time n years,
then,
8 = (1+(r/100))n;
23 = (1+(r/100))n; .. (ii)
Using eqn (i) in (ii), we get;
([1+(r/100)]4)3 = (1+(r/100))n;
[1+(r/100)]12 = (1+(r/100))n;
Thus, n = 12 years.

Arun took a loan of Rs. 1400 with simple interest for as many years as the rate of interest. If he paid Rs.686 as interest at the end of the loan period, what was the rate of interest?
  • a)
    8%
  • b)
    6%
  • c)
    4%
  • d)
    7%
Correct answer is option 'D'. Can you explain this answer?

Meghana Mishra answered
Simple Interest (SI) = P N R / 100
P is the Principal loan amount = Rs.1400
N is the number of years of deposit
R is the rate of interest
It is given that the loan period is as many years as the rate of interest.
So, N = R
Interest at the end of the loan period (SI ) = Rs.686
So,
686 = 1400 * R * R /100
R^2 = 686*100 /1400
R^2 = 49
R = 7%

The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is
  • a)
    5
  • b)
    4
  • c)
    6
  • d)
    2
Correct answer is option 'B'. Can you explain this answer?

Anaya Patel answered
P [1 + (r/100)]n  >  2P
⇒ P [1 + (20/100)]n  >  2P
[1 + (2/10) ]n  > 2
[12 / 10]n  > 2
[6/5]n  > 2
{6/5 * 6/5 * 6/5 * 6/5}  >  2
∴ n = 4
 

A man took loan from a bank at the rate of 8% p.a. simple interest. After 4 years he had to pay Rs. 6200 interest only for the period. The principal amount borrowed by him was:
  • a)
    Rs.17322
  • b)
    Rs.20245
  • c)
    Rs.18230
  • d)
    Rs.19375
Correct answer is option 'D'. Can you explain this answer?

Aarav Sharma answered
Given:
Rate of interest = 8% p.a.
Interest paid after 4 years = Rs. 6200

To find: Principal amount borrowed

Formula: Simple Interest = (P * R * T) / 100

Where,
P = Principal amount
R = Rate of interest
T = Time (in years)

Calculation:
Let the principal amount be P.

Simple Interest for 4 years = Rs. 6200
=> (P * 8 * 4) / 100 = Rs. 6200
=> 32P = 620000
=> P = Rs. 19375

Therefore, the principal amount borrowed was Rs. 19375.

What will be the compound interest on a sum of Rs. 40,000 after 3 years at the rate of 11 p.c.p.a.? 
  • a)
    Rs. 14705.24
  • b)
    Rs. 14602.25
  • c)
    Rs. 14822.26
  • d)
    Rs. 14322.10
Correct answer is option 'A'. Can you explain this answer?

Rhea Reddy answered
Amount after 3 years = P(1 + R/100)T
=> 40000(1 + 11/100)3
=> 40000(111/100)3
=> 40000[(111*111*111)/(100*100*100)]
=> (4*111*111*111)/100 
=> 54705.24
Compound Interest = 54705.24 - 40000 
= Rs. 14705.24

The Simple interest on a certain sum for 2 years at 20% per annum is Rs. 80. The corresponding compound interest is 
  • a)
    Rs. 66
  • b)
    Rs. 82
  • c)
    Rs. 86
  • d)
    Rs. 88
Correct answer is option 'D'. Can you explain this answer?

Savitri Verma answered
Time =2. rate =20%. p=? SI =80
p=SI*100/R*T p=80×100/20×2
p=200. A=p(1+R/100)^n
A=200(1+20/100)^2
A=200×12×12/100×100
A=288
( CI=A-P)
CI =288-200 = 88

A sum of Rs. 600 amounts to Rs. 720 in 4 years at Simple Interest. What will it amount to if the rate of interest is increased by 2%?
  • a)
    Rs. 648
  • b)
    Rs. 768
  • c)
    Rs. 726
  • d)
    Rs. 792
Correct answer is option 'B'. Can you explain this answer?

Alok Kapoor answered
600 becomes 720 in 4 years SI —> SI per year = Rs. 30 and hence the SI rate is 5%.
At 7% rate of interest the value of 600 would become 768 in 4 years. (600 + 28% of 600)

What annual payment will discharge a debt of Rs. 6450 due in 4 years at 5% per annum?
  • a)
    Rs.1800
  • b)
    Rs.1400
  • c)
    Rs.1500
  • d)
    Rs.1600
Correct answer is option 'A'. Can you explain this answer?

Dhruv Mehra answered
We have to find the annual payment that will discharge a debt of Rs. 6450 in 4 years at a 5% per annum interest rate. We can solve this problem using the annuity formula.

The annuity formula is given by:

P = (R * (1 - (1 + r)^(-n))) / r

Where P is the present value (amount of the debt), R is the annual payment, r is the interest rate per period, and n is the number of periods.

In this problem, P = 6450, r = 5% = 0.05, and n = 4.

We need to find R.

6450 = (R * (1 - (1 + 0.05)^(-4))) / 0.05

Now, let's solve for R.

6450 = (R * (1 - (1.05)^(-4))) / 0.05

6450 = (R * (1 - 0.822702)) / 0.05

6450 = (R * 0.177298) / 0.05

Now, multiply both sides by 0.05.

6450 * 0.05 = R * 0.177298

Now, divide both sides by 0.177298.

(6450 * 0.05) / 0.177298 = R

R ≈ 1816.61

Since we need to find the closest integer value for the annual payment, we can round it to Rs. 1800.

So, the correct answer is Rs. 1800

Ajay borrows Rs. 1500 from two moneylenders. He pays interest at the rate of 12% per annum for one loan and at the rate of 14% per annum for the other. The total interest he pays for the entire year is Rs. 186. How much does he borrow at the rate of 12%?
  • a)
    Rs. 1200
  • b)
    Rs. 1300
  • c)
    Rs. 1400
  • d)
    Rs. 300
Correct answer is option 'A'. Can you explain this answer?

Aarav Sharma answered
Given:
Ajay borrows Rs.1500 from two moneylenders.
He pays interest at the rate of 12% per annum for one loan and at the rate of 14% per annum for the other.
The total interest he pays for the entire year is Rs.186.

To Find: How much does he borrow at the rate of 12%?

Solution:
Let's assume that Ajay borrows x rupees at 12% per annum and (1500 - x) rupees at 14% per annum.

According to the question,
Total interest paid = Rs.186

Therefore,
Interest on x rupees at 12% per annum + Interest on (1500 - x) rupees at 14% per annum = Rs.186

=> (x * 12 * 1/100) + ((1500 - x) * 14 * 1/100) = 186

=> 12x/100 + 21000/100 - 14x/100 = 186

=> -2x/100 = -24

=> x = (100 * 24)/2 = 1200

Hence, Ajay borrows Rs. 1200 at the rate of 12%. Therefore, option A is the correct answer.

If a sum of Rs. 9 is lent to be paid back in 10 equal monthly installments of re. 1 each, then the rate of interest is
  • a)
    11.33%
  • b)
    11%
  • c)
    266.67%
  • d)
    33.33%
Correct answer is option 'D'. Can you explain this answer?

Manoj Ghosh answered
Let's try to understand the problem step by step.

A sum of Rs. 9 is lent to be paid back in 10 equal monthly installments of Re. 1 each.

This means that the borrower is paying back Re. 1 per month for 10 months.

Now, let's calculate the interest paid in each installment.

1. In the first month, the borrower still owes Rs. 9, so no interest is paid.
2. In the second month, the borrower has already paid Re. 1, so he now owes Rs. 8. The interest paid would be on Rs. 8.
3. In the third month, the borrower has paid Rs. 2, so he now owes Rs. 7. The interest paid would be on Rs. 7.
4. This continues until the 10th month when the borrower has paid Rs. 9 and owes nothing.

Now let's calculate the total interest paid over the 10 months.

Total Interest Paid = (Interest on Rs. 8) + (Interest on Rs. 7) + ... + (Interest on Re. 1)

Let's assume the rate of interest is "R" percent per month.

Total Interest Paid = (8 * R) + (7 * R) + ... + (1 * R)

Now, we know that the total amount paid is Rs. 10 (10 installments of Re. 1 each), and the total amount lent is Rs. 9. So, the total interest paid is Rs. 1.

1 = (8 * R) + (7 * R) + ... + (1 * R)

Now we can simplify the equation:

1 = R * (8 + 7 + 6 + 5 + 4 + 3 + 2 + 1)

1 = R * 36

Now, let's find the value of R (the rate of interest per month):

R = 1/36

Since we need to calculate the rate of interest in percentage, we multiply R by 100:

R (%) = (1/36) * 100 = 2.78%

Now, we have the monthly rate of interest. To find the annual rate of interest, we multiply the monthly rate by 12:

Annual Rate of Interest = 2.78% * 12 = 33.33%

Find the compound interest at the rate of 10% for 3 years on that principal which in 3 years at the rate of 10% per annum gives Rs. 300 as simple interest.
  • a)
    Rs. 331
  • b)
    Rs. 310
  • c)
    Rs. 330
  • d)
    Rs. 333
Correct answer is option 'A'. Can you explain this answer?

Poulomi Sarkar answered
At 10% per annum simple interest, the interest earned over 3 years would be 30% of the capital. Thus, 300 is 30% of the capital which means that the capital is 1000. In 3 years, the compound interest on the same amount would be 331.

Find the compound interest on Rs. 1000 at the rate of 20% per annum for 18 months when interest is compounded half-yearly.
  • a)
    Rs. 331
  • b)
    Rs. 1331
  • c)
    Rs. 320
  • d)
    Rs. 325
Correct answer is option 'A'. Can you explain this answer?

Given that,
p = ₹1000
r = 20% = 0.2%
n = 2 times
t = 1.5 year (because 18 month equal to 1 year and half of a year.)

So A = 1000 ( 1 + 0.2/2 )^2 X 1.5
= 1000 ( 2.2/2 )^2 X 3 / 2
= 1000 ( 22 / 20 )^3
= 1000 X(22 X 22 X 22 ) / ( 20 X 20 X 20 )
= ( 22X 22 X 22 ) / 8
= 10648 / 8
= 1331

So after 18 years the accumulated amount will be ₹1331.
CORRECT OPTION IS (b).

Chapter doubts & questions for Partnerships - Arithmetic Ability for DSSSB exams 2024 is part of DSSSB TGT/PGT/PRT exam preparation. The chapters have been prepared according to the DSSSB TGT/PGT/PRT exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for DSSSB TGT/PGT/PRT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

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