Question

Mrs. Seema lends 30% of sum at 15% per annum. 50% of the rest sum at 12% p.a. and the
remaining at 8% p.a. rate of interest. What would be the rate if the interest is calculated on
the whole sum?​

Answer 1

Given :     Mrs. Seema lends 30% of sum at 15% per annum.

50% of the rest sum at 12% p.a. and the

remaining at 8% p.a. rate of interest.

To Find : What would be the rate if the interest is calculated on the whole sum?​

Solution:

Let say sum = 100X

30% of sum at 15% per annum.  =>  (30/100)100X = 30X

Remaining = 70X

50% of the rest sum at 12% p.a. and the

=> (50/100)70X  = 35X

Rest amount = 100X - 30X - 35X  =  35X at 8 % pa

Interest = P * R * T / 100

= 30X * 15 *  1 / 100   +  35X * 12 * 1/100  + 35X * 8 * 1/100

= X(4.5 + 4.2 + 2.8)

=  X ( 11.5)  

Rate of interest = 11.5 %

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Answer 2

Given:

Mrs. Seema lends 30% of the sum at 15% per annum. 50% of the rest sum at 12% p.a. and the remaining at 8% p.a. rate of interest.

To find:

What would be the rate if the interest is calculated on the whole sum?​

Solution:

For easy calculation let us consider the whole sum of money as "Rs. 100".

Finding interest on 30% of the sum:

30% of the sum = $\frac{30}{100} \times 100 = Rs. \:30$

The rate of interest = 15% p.a.

The no. of years = 1 year

∴ S.I. on Rs. 30 for 1 year = $\frac{P\times R \times T }{100} = \frac{30 \times 15 \times 1}{100} = Rs. 4.5$

Finding interest on 50% of the rest sum:

Rest of the sum = Rs. 100 - Rs. 30 = Rs. 70

50% of the rest of the sum = $\frac{50}{100} \times 70 = Rs. \:35$

The rate of interest = 12% p.a.

The no. of years = 1 year

∴ S.I. on Rs. 35 for 1 year = $\frac{P\times R \times T }{100} = \frac{35 \times 12 \times 1}{100} = Rs. 4.2$

Finding interest on the remaining sum:

Rest of the sum = Rs. 70 - Rs. 35 = Rs. 35

The rate of interest = 12% p.a.

The no. of years = 1 year

∴ S.I. on Rs. 35 for 1 year = $\frac{P\times R \times T }{100} = \frac{35 \times 8 \times 1}{100} = Rs. 2.8$

Therefore,

The interest earned on the whole sum of Rs. 100 for 1 year is,

= 4.5 + 4.2 + 2.8

= Rs. 11.5

Now,

The rate of interest on the whole sum of Rs. 100 for 1 year will be,

= $\frac{11.5}{100} \times 100$

= $\bold{11.5\%}$

Thus, the rate, if the interest is calculated on the whole sum of money would be → 11.5%.

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