## Exercise 9 (A)

QUESTION 1

What will be the simple interest for 1 year 4 months on a sum of 25800 at the rate of 14% p.a. ?

Sol :

We know

= 4816

QUESTION 2

What will 5000 amount to at 8% p.a. for the period from april 6 , 2017 to june 18 , 2017 ?

Sol :

Lets find time period (T)

12 days and 2 months ( may month have 31 days)

12 days and 2 month = 73 days

= 80

Amount = Principal + Interest

= 5000 + 80

= 5080

QUESTION 3

A sum of 3200 becomes 3456 in two years at a certain rate of simple interest . What is the rate of interest per annum ?

Sol :

T = 2 year , R = ? , P = 3200

After adding simple interest to principal = 3456

S.I = 3456 – 3200 = 256

R = 4

R = 4 % per annum

QUESTION 4

Find the principal on which a simple interest of 56 will be obtained after 9 months at the rate of per annum ?

Sol :

P = 2036.36

QUESTION 5

In what time will 1860 amount to 2641.20 at simple interest of 12% per annum ?

Sol :

T = ? , P = 1860 , R = 12 % per annum

S.I = 2641.20 – 1860 = 781.2

years

QUESTION 6

Firoz invested a sum of money at an annual simple interest rate of 10% . At the end of 4 years , the amount received by Firoz was 7700 . What was the sum invested ?

Sol :

P = ? , R = 10% per annum , T = 4 years , I = ?

Let the principal be x

Amount = Principal + Interest

x = 5500

Which means Principal = 5500 , Firoz invested 5500 rupees

QUESTION 7

A person deposited 400 for 2 years , 550 for 4 years and 1200 for 6 years at the same rate of simple interest . If he received a total interest of 1020 . What is the rate of interest per annum ?

Sol :

Let the rate of interest be R per annum

According to question ,

8R + 22R + 72R = 1020

102R = 1020

R = 10% per annum

QUESTION 8

The simple interest on a certain sum for 8 months at 4% is 129 less than the simple interest on the same sum for 15 months at 5% per annum . What is the sum ?

Sol :

Let the Principal be P

T1 =

T2 = 15 months = 12 months + 1 month

= 1 year + 1 month

T2 =1+\dfrac{1}{12}

T2

According to question

P = 3600

So , the sum is 3600

QUESTION 9

The simple interest on a sum of 5 years is one-fourth of the sum . What is the rate of interest per annum ?

Sol :

T = 5 years , R = ? , , P = P

R = 5 % per annum

QUESTION 10

Simple interest on a certain sum is of the sum . Find the time (in years) . If the rate per cent and time are equal ?

Sol :

x^{2} = 64

x = 8

Which means R = 8 , T = 8 years

QUESTION 11

At a certain rate of simple interest , a certain sum of money becomes double of itself in 10 years . In what time will it becomes treble of itself ?

Sol :

Let Principal be P and Rate of interest be R

Amount = 2P (given)

Amount = Principal + Interest

2P = P + I

I = P

And Time period (T) = 10 years

So ,

R = 10 % per annum

Now , the second case where Amount become triple

Amount = 3P (given)

Amount = Principal + Interest

3P = P + I

I = 2P

Putting this in formula we get

T = 20 years

QUESTION 12

A part of 1500 was lent at 10% per annum and the rest at 7% per annum simple interest . The total interest earned in 3 years was 396 . What was the sum lent at 10% p.a. ?

Sol :

Here , we have two cases

Case 1 : Let the principal be P and R = 10 and T = 3

Case 2 : Let the principal be ( 1500 – P ) , R = 7 and T = 3

Then adding interest of both the cases , which is equal to total interest

30P + 31500 – 21P = 39600

9P = 8100

P = 900