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Test: Simple Interest- 2 - UPSC MCQ


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10 Questions MCQ Test CSAT Preparation - Test: Simple Interest- 2

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Test: Simple Interest- 2 - Question 1

A sum of Rs. 14,000 amounts to Rs. 22,400 in 12 years at the rate of simple interest. What is the rate of interest?

Detailed Solution for Test: Simple Interest- 2 - Question 1

Amount = 22400, P = 14000, T = 12yrs
SI = 22400 - 14000
= 8400
Rate = (8400*100)/(12*14000)
= 5%
 

Test: Simple Interest- 2 - Question 2

A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest?

Detailed Solution for Test: Simple Interest- 2 - Question 2

Test: Simple Interest- 2 - Question 3

An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:

Detailed Solution for Test: Simple Interest- 2 - Question 3

B is the correct option. Solution
6 months interest will be 5%
next 6 months interest will be 5%
percentage effect = 5 + 5 +25/100
= 10.25 Ans
 

Test: Simple Interest- 2 - Question 4

A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:

Detailed Solution for Test: Simple Interest- 2 - Question 4

Let the rate of interest be x% per annum.
For the loan to B:
Simple interest = (5000)(2)(x)/100 = 100x
For the loan to C:
Simple interest = (3000)(4)(x)/100 = 120x
Total simple interest received = 100x + 120x = 220x
Given, 220x = 2200
x = 10
Therefore, the rate of interest per annum is 10%.

Test: Simple Interest- 2 - Question 5

What annual payment will discharge a debt of Rs. 6450 due in 4 years at 5% per annum?

Detailed Solution for Test: Simple Interest- 2 - Question 5

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

Test: Simple Interest- 2 - Question 6

A lends Rs. 1500 to B and a certain sum to C at the same time at 8% per annum simple interest. If after 4 years, A altogether receives Rs. 1400 as interest from B and C, then the sum lent to C is A.

Detailed Solution for Test: Simple Interest- 2 - Question 6

A is the correct option.
Simple interest on the total money lent at 
8% FOR 4 YEARS = 1400
Total money lent
= 100/8 × 1400/4 =4375
Therefore, money lent to C
= 4375- 1400 = 2875

Test: Simple Interest- 2 - Question 7

If the simple interest on a certain sum of money after 3 1/8 years is 1/4 of the principal, what is the rate of interest per annum?

Detailed Solution for Test: Simple Interest- 2 - Question 7

Take P=x
given T=25/8
& I=1/4x
w.k.t I=PTR/100
1/4x =x*25/8*R/100
R = 8%

Test: Simple Interest- 2 - Question 8

A sum of Rs. 10 is lend to be returned in 11 monthly instalments of Rs. 1 each, interest being simple. The rate of interest charged is:

Detailed Solution for Test: Simple Interest- 2 - Question 8

Given :

A sum of Rs. 10 is lend to be returned in 11 monthly instalments of Rs . 1 each interest being simple 

Formula used :

Simple interest = P × R× T /100 

Principal(P), Rate(R) and Time(T)

Calculation :

Let the rate of interest be R% per annum

⇒ Amount to be paid (if paid at the end of 11 months)

⇒ 10 + [10 × R × (11/12) / 100] = 10 + (11R/120)

⇒ Total effective payment = (Rs. 1 + interest on Rs. 1 for 10 months) + (Rs. 1 + interest on Rs. 1 for 9 months) + .... +(Rs. 1 + interest on Rs. 1 for 1 months) + Rs. 1

⇒ (1 + 1 × R × (10/12) / 100)   + (1 + 1 × R × (9/12) / 100) + .... + (1 + 1 × R × (1/12) / 100) + 1

⇒ (1 + 10R/1200) + (1 + 9R/1200) + .... + (1 + R/1200) + 1

⇒ 11 + R(1 + 2 + .... + 10)/1200

⇒ 11 + R(10 × 11 / 2)/1200

⇒ 11 + R(10 × 11 / 2)/1200

⇒ 11 + 11R/240 

Now we have, 

⇒ 10 + 11R/120 = 11 + 11R/240

⇒ 11R/240 = 1

⇒ R = 240/11 = 21× 9/11%

∴ Rate of interest is 21(9/11)%

Test: Simple Interest- 2 - Question 9

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

Detailed Solution for Test: Simple Interest- 2 - Question 9

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%

Test: Simple Interest- 2 - Question 10

Divide Rs. 2379 into 3 parts so that their amount after 2,3 and 4 years respectively may be equal, the rate of interest being 5% per annum at simple interest. The first part is

Detailed Solution for Test: Simple Interest- 2 - Question 10

The correct answer is D  as
let assume 3 parts of amount are x,y,z
x+y+z=2379
SI for x= x*5*2/100⇒ x/10
Total amount after 2 years - x+(x/10)= 11x/10 ------------(1)
SI for y= y*5*3/100=> 15y/100
Total amount after 3 years - y+(15y/100) = 115y/100 -------(2)
SI for z= z*5*4/100=> z/5
Total amount after 4 years - z+(z/5) = 6z/5 ---------------(3)

As per the conditions "3 parts amounts after 2, 3 and 4 years respectively may be equal" (1) = (2) = (3)
based on the above condition and x+y+z=2379, we can get x= 828, y= 792 and z= 759
So answer is Rs.828

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