Question

Balu borrowed 4000 from Bhabi at 10% p.a simple interest for four years. He then added some more money to the borrowed sum and lent it to Babloo for the same time at 15% p.a simple interest. If Balu gains 1400 by way of interest on the borrowed sum as well as his own amount from the whole transaction, then what is the sum lent by him to Babloo?

Answer 1

Step-by-step explanation:

Given :-

Balu borrowed 4000 from Bhabi at 10% p.a simple interest for four years. He then added some more money to the borrowed sum and lent it to Babloo for the same time at 15% p.a simple interest.

To find:-

If Balu gains 1400 by way of interest on the borrowed sum as well as his own amount from the whole transaction, then what is the sum lent by him to Babloo?

Solution:-

Borrowed money from Bhabi by Balu = Rs. 4000

Rate of interest = 10%

Time = 4 years

We have ,

P = Rs. 4000

T = 4 years

R = 10%

We know that

Simple Interest (SI) = PTR/100

=> (4000×4×10)/100

=> 160000/100

=> 1600

So , Simple Interest = Rs. 1600

Amount = Principle+Interest

=> A = 4000+1600

Amount = Rs. 5600

Total amount to be paid to Bhabi by Balu after 4 years = Rs. 5600

Let the money adde to Rs. 4000 be Rs. X

Then total money = Rs. (4000+X)

The money is lent to Babloo = Rs. (4000+X)

Rate of interest = 15%

Time = 4 Years

We know that

Simple Interest (SI) = PTR/100

=> (4000+X)×4×15/100

=> (4000+X)×60/100

=> (4000+X)×3/5

=>( 12000+3X)/5

So , Simple Interest = Rs. ( 12000+3X)/5

Amount = Principle+Interest

=> A = (4000+X)+(12000+3X)/5

=> A = [5(4000+X)+(12000+3X)]/5

=> A = (20000+5X+12000+3X)/5

=> A = (32000+8X)/5

Amount = Rs.(32000+8X)/5

Total amount to be paid to Balu by Babloo after 4 years = Rs. (32000+8X)/5

Given that

If Balu gains 1400 in whole translation then

Rs. (32000+8X)/5 - Rs. 5600 = Rs. 1400

=> (32000+8X)/5 -5600 = 1400

=> (32000+8X)/5 = 1400+5600

=> (32000+8X)/5 = 7000

=> 32000+8X = 7000×5

=> 32000+8X = 35000

=> 8X = 35000-32000

=> 8X = 3000

=> X = 3000/8

=> X = 375

Therefore , X = Rs. 375

The money is lent to Babloo = Rs. 4000+X

=> 4000+375

=> Rs. 4375

Answer:-

The money is lent to Babloo by Balu = Rs. 4375

Used formulae:-

• Simple Interest = PTR/100

• Amount = Principle+Interest

• P = Principle

• T = Time

• R = Rate of interest