Simple Interest set 1

Simple Interest set 1

Simple Interest set 1
A final amount
P initial principal balance
r annual interest rate
t time (in years)

Read the following questions carefully and choose the right answer.

1] From a bank, Ram and Shyam together took a certain amount under SI
and they lent the total amount to Mohan at 2% more SI. At the end of 4
years, the total money earned by Ram after paying the interest to the bank was Rs. 400 more than that of Shyam. From the bank, the total amount taken by Ram was how much more than that of Shyam?
A. Rs. 10000
B. Rs. 20000
C. Rs. 5000
D. Rs. 25000
E. Can’t be determined

Let Ram took Rs. a and Shyam took Rs. b
Let the rate of interest was r% per annum

They lent Rs. (a + b) to Mohan at the rate of (r + 2)% per annum

For Ram,

The total interest received on Rs. a = a
× 4 × (r + 2)/100
The total interest paid by Ram to the bank = a × r ×
4/100
The total interest earned by Ram after paying the interest to the bank

= a × 4 ×
(r + 2)/100 a × r × 4/100 = 8a/100 —— (i)

For Shyam,

The total interest received on Rs. b = b × 4 ×
(r+ 2)/100
The total interest paid by Shyam to the bank = b × r ×
4/100
The total interest earned by Ram after paying the interest to the bank

= b × 4 ×
(r + 2)/100 b × r × 4/100 = 8b/100 —— (ii)

From the question,

8a/100
8b/100 = 400

a b = 50 × 100 = Rs. 5000
Hence, option C is correct.

2] Rayan invested a total of Rs.49000 in two different schemes A and B. The scheme A which offers interest at a rate of 5% per annum and scheme B offers interest at a rate of 12%. If the total interest earned by Rayan after 1 year is Rs.4900 then find the sum invested in scheme B.
A. Rs. 34000
B. Rs. 19000
C. Rs. 35000
D. Rs. 14000
E. Rs. 30000

Let the total investment in scheme B be Rs.x, then
(49000
X) × 5/100 + X × 12/100 = 4900

X =
5/7 × 49000 = Rs. 35000

Hence, option C is correct.

3] After four years, the SI obtained on Rs. 8250 at the rate of (x + 4)% is Rs. 1320 more than the SI obtained at the rate of 8% per annum. Find the
value of ‘x’.

A. 12%
B. 10%
C. 8%
D. 15%
E. None of these

According to the question,
8250 × (x + 4) % × 4
8250 × 8% × 4 = 1320
330 (x + 4)
2640 = 1320
330 (x + 4) = 3960

x + 4 = 12 ;
x = 8
So, the value of x = 8%

Hence, option C is correct.

4] Aman and Raghav are two friends. Aman started a business with an investment of Rs 7200, while Raghav puts 60% of his salary at 40% p.a SI for 6 months; Raghav takes the amount received after 6 months and joins Aman in the business. If Aman receives a profit of Rs. 2000 out of a total profit of Rs. 2900 at the end of 1 year, what was the original salary of Raghav?
A. Rs. 18000
B. Rs. 9400
C. Rs. 9000
D. Rs. 15000
E. None of these

Ratio of profit = 2000 : 900 = 20 : 9
Let amount invested by Raghav be K

Ratio of inves
tment = 12 × 7200 : 6 × K = 14400 : K = 20 : 9
K = Rs 6480

Let original Salary of Raghav = R

60 %( R) at 40% p.a for 6 months

60
× R × 40 × 1 = 6480 – 0.6R
100
200
R = Rs. 9000

Hence, option C is correct.

5] A sum of Rs. 12,000 invested at 8% SI becomes Rs. 15840 in x years and
another sum of Rs. 15,000 invested at 12% SI becomes Rs. 18,600 in y
years. Find the value of x + y.

A. 6
B. 7
C. 5
D. 8
E. 10

1st Case :
Interest
= A P = 3840
Now, I =
P × R × N
100

3840 =
(12000 × 8 × x)/100
x = 4
2nd Case :
Interest = 18600 15000 = 3600

3600 =
(15000 × 12 × y)/100
y = 2
x + y = 4 + 2 = 6
Hence, option A is correct.

 

NOTE: SI stands for Simple Interest

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