Question

Rs.16000 is lent in two parts. A part is lent at 10% p.a. and the other part is lent at 20% p.a. Both parts are lent at simple interest for a year. The total interest realized from them is Rs.1920. Find the difference of the parts (in Rs).

Answer 1

Let first part = Rs. x
2nd part = Rs. (16000 - x)

case 1 :- P = x ,
rate of interest , r = 10% pa
time , t = 1 yr
S.I = P × r × t/100 = x × 10 × 1/100 = x/10

Case 2 :- P = (16000 - x)
rate of interest , r = 20% pa
time , t = 1 yr
S.I = P × r × t/100 = (16000 - x) × 20 × 1/100 = (16000 - x)/5

A/C to question,
Total interest = Rs. 1920
∴ x/10 + (16000 - x)/5 = 1920
⇒ {x + 2(16000 - x)}/10 = 1920
⇒ {x + 32000 - 2x} = 19200
⇒ 32000 - x = 19200
⇒ 32000 - 19200 = x
⇒x = 12800

Hence, first part = Rs. 12800
2nd part = 16000 - 12800 = Rs. 3200

Answer 2

Hello Dear.

Here is your answer---


Let the First part in which Rs.16000 is divided be x.

Thus, Second Part = (16000 - x).

For First Part, 
 
R% = 10%
 Time(T) = 1 year.
Principal(P) = Rs. x

Thus, Interest = $\frac{PRT}{100}$

               Interest = (x × 10 × 1) ÷ 100
                 Interest = x/10

For second Part,
Principal(P) = Rs. (16000 -x)
 
Rate of Interest(R%) = 20 %
Time(T) = 1 Year

Thus, Interest = ({16000 - x} × 20 × 1) ÷ 100
                       = $\frac{16000 - x }{5}$

According to the Question,
 
       Interest in first part + Interest in second part = Rs. 1920
 
⇒ $\frac{x}{10}$ + $\frac{16000 - x }{5}$ = 1920

⇒  $\frac{x + 32000 - 2x }{10}$ = 1920

⇒  $\frac{32000 - x}{10}$ = 1920

⇒ 32000 - x = 1920 × 10

⇒ x = 32000 - 19200

⇒ x = Rs. 12800

Thus, First Part  =  x
                          =  Rs.12800

∴ Second Part = 16000 - x
                        = 16000 - 12800
                        = Rs. 3200


Thus, Difference of the Parts = 12800 - 3200
                                               = Rs. 9600


Hope it helps.

Have a marvelous day.