Question

Mr Hamid and Mr Ali borrowed the same amount on the same date from co - operative bank on the condition that if the loan be repayed with interest within 3 yrs, the rate of interest would be 6℅ per annum but it would be charged at 7.5% if 3 yrs be exceeded. Mr Hamid and Mr. Ali repayed their loans at the end of 3 yrs and 5 yrs respectively. If Mr. Ali had to pay Rs.4875 more as interest, find the sum borrowed by each.​

Answer 1

Given :

Mr Hamid and Mr Ali borrowed the same amount on the same date from co - operative bank on the condition that if the loan be repaid with interest within 3 yrs, the rate of interest would be 6℅ per annum but it would be charged at 7.5% if 3 yrs be exceeded. Mr Hamid and Mr. Ali repayed their loans at the end of 3 yrs and 5 yrs respectively. If Mr. Ali had to pay Rs.4875 more as interest.

To find :

Sum borrowed by each.

Solution :

Let the sum borrowed by each be Rs. P

And let the interest paid by Mr. Hamid be Rs. x

∴ Interest paid by Mr. Ali = Rs. (x + 4875)

Now in the case of Mr. Hamid :

SI = (P * r * n)/100

⇒ x = (P * 6 * 3)/100

⇒ x = 18P/100

⇒ 18P = 100x

⇒ P = 100x/18

⇒ P = 50x/9                       _(i)

In the case of Mr. Ali :

⇒ x + 4875 = (P * 7.5 * 5)/100

⇒ 100(x + 4875) = 37.5P

⇒ P = 100(x + 4875)/37.5                   _(ii)

Now comparing (i) and (ii) :

⇒ 50x/9 = 100(x + 4875)/37.5

⇒ 1875x = 900(x + 4875)

⇒ 1875x = 900x + 4387500

⇒ 1875x - 900x = 4387500

⇒ 975x = 4387500

⇒ x = 4387500/975

⇒ x = 4500

∴ Interest paid by Mr. Hamid , x = Rs. 4,500.

Now putting value of x in (i) :

⇒ P = (50 * 4500)/9

⇒ P = 225,000/9

⇒ P = 25,000

Therefore,

Sum borrowed by each = Rs. 25,000.

Answer 2

Step-by-step explanation:

Given :

• interest within 3 yrs, the rate of interest would be 6℅ per annum .

• it would be charged at 7.5% if 3 yrs be exceeded.

• Mr Hamid and Mr. Ali repayed their loans at the end of 3 yrs and 5 yrs respectively.

• Mr. Ali had to pay Rs.4875 more as interest.

To find :

• Find the sum borrowed by each.

Solution :

Let the sum borrowed by each be Rs. P

And let the interest paid by Mr. Hamid be Rs. x

Interest paid by Mr. Ali = 4875 × 3 × 6 / 100

Interest paid by Mr. Ali = 390

Mr. Ali repayed their loans at the end of 3 yrs and 5 yrs respectively. :

= 5 × 3

= 15

= 4875 - 390

Mr. Hamid be Rs. x = 4485 + 15

Mr. Hamid be Rs. x = 4500

SI = (P × r × n)/100

4500 = (P × 6 × 3)/100

4500 = 18P/100

18P = 100 × 4500

P = 450000/18

P = 25,000

Hence the sum borrowed by each. 25,000 RS.