**Advertisements**1. A sum becomes two times in 5 year at a certain rate of interest . Find the time in which the same

amount will be 8 times at the same rate of interest?

1) 35 year 2) 45 year 3) 55 year 4) 25 year 5) None of these

Solution: (1).

Here, n = 2 , m=8,

T1 = 5,

T2 = ?

Therefore T2 = ( (m – 1) / (n – 1) ) X T1 = ( (8 - 1) / ( 2 – 1 ) X 5 = 35 year

2. A certain sum in certain time becomes Rs.500 at the rate of 8 % per annum Simple Interest and the

same sum amounts to Rs.200 at the rate of 2% per annum Simple Interest in the same duration. Find the

sum and time.

1) Rs.100 and 50yr 2) Rs.200 and 25 yr 3) Rs.300 and 30 yr 4) Rs.400 and 35 year 5) None of these

Solution: (1). Here, R1 = 8% , R2 = 2% , A1 = Rs.500, A2 = Rs.200

Now, according to the formula,

P = ( A2R1 – A1R2) / ( R1 – R2) = (200 x 8 – 500 x 2 ) / (8 - 2) = (1600 – 1000) / 6

= 600/6

= Rs. 100

And

Time, T = (A1 – A2) / (A2R1 – A1R2) X 100

= ( 500 – 200 ) / ( 200 x 8 – 500 x 2 ) x 100

= 300 / 600 x 100

= 50 year

3. Simple interest for a sum of Rs.1550 for 2 year is Rs.20 more than the simple interest for Rs.1450 for

the same duration. Find the rate of interest.

1) 10% 2) 20% 3) 25% 4) 15% 5) None of these

Solution: (1). Given that, P1 = Rs. 1550, T1 = 2, P2 = Rs.1450, T2 = 2

According to the question,

= [ (P1 x R x T1) / 100 ] - [ (P2 x R X T2 ) / 100 ] = 20

= [ ( 1550 x 2 x R ) / 100 ] - [ ( 1450 x 2 x R ) / 100 ] = 20

= 200R / 100 = 20

R = 10%

4. 2/3 part of my sum is lent out at 3%, 1/6 part is lent out at 6% and remaining part is lent out at 12% .

All the three parts are lent out at simple interest. If the annual income is Rs.25, what is the sum?

1) Rs.500 2) Rs.650 3) Rs. 600 4) Rs. 450 5) None of the these

Solution: (1).

Let entire sum = P

According to the question,

2/3 P X 3% + 1/6 P X 6% + [ 1- ( 2/3 + 1/6) ] P x 12%

= 2P/3 X 3/100 + P/6 x 6/100 + [ 1 – (4+1) / 6 ] 12P / 100 = 25

= 2P / 100 + P/100 + 2P/100 = 25

= 5P = 2500, P = 500

5. The simple interest on a sum of money is 1/16 of the principal and the number of years is equal to

the rate per cent annum. Find the rate per cent .

1) 2 ½ % 2) 3 ½ % 3) 4 ½ % 4) 9 ½ % 5) None of these

Solution: (1). Let Principal = P , Time = T and rate = T

According to the question,

( P X T X T ) / 100 = P / 16

(since time and rate are equal )

= T2 = 100 / 16 or T = 10/4 = 5/2 = 2 ½ %

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