Test: Simple Interest- 2 - UPSC MCQ

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

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
 

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%.

Installment for first year = x

Installment for second year = 1.10x

Installment for third year = 1.20x

Installment for third year = 1.30x

Installment for final year = 1.40x

Total amount to be paid = (1 + 1.10 + 1.20 + 1.30 + 1.40) × x = 6450

∴ x = 6450 / 6 = 1075

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- 1500 = 2875

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%

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)%

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%

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