Question

A man lent a part of money at 10% p.a. and the rest at 15% p.a. his annual income Rs1900. If he had interchanged the rate of interest on two sums, he would have earned Rs200 more. Find the amount lent in each case.

Plz gys answer this

Answer 1

heya friend!!☺☺
here's your answer!!☺☺

Let , Man lent a part of money at 10% p.a. = x
And
Man lent a part of money at 15% p.a. = y

So,

From first condition ,we get

10 x100 + 15 y100 = 1900
⇒x10 + 3 y20 = 1900
⇒2 x + 3 y 20 = 1900
⇒2 x + 3 y = 38000 −−−− ( 1 )

And also given : If he had interchanged the rate of interest on two sums , he would have earned Rs.200 more . So

10 y100 + 15 x100 = 1900
⇒y10 + 3 x20 = 1900
⇒2 y + 3 x 20 = 1900
⇒2 y + 3 x = 38000 −−−− ( 2 )

Now we multiply by 3 in equation 1 and multiply by 2 in equation 2 , we get

6x + 9y = 114000 ----- ( 4 )
And
4y + 6x = 84000 ----- ( 5 )

Now we subtract equation 5 from equation 4 and get

5y = 30000

y = 6000 , Substitute that value in equation ( 1 ) and get

2x + 3 ( 6000 ) = 38000

2x + 18000 = 38000

2x = 20000

x = 10000

So,

Man lent a part of money at 10% p.a. = Rs. 10, 000
And
Man lent a part of money at 15% p.a. = Rs. 6,000

hope it helps you!!☺☺

Answer 2

Let the amounts invested at 10% and 15% be x and y rupees
Then SI on x at 10% for 1 year =x*10*1/100
=x/10

SI on y at 15% for 1 year
=y*15*1/100
=3y/20

ATQ, x/10+3y/20=1900
Taking lcm we get
(2x+3y)/20=1900
2X+3y=38000.........1

Case2
When x and y are interchanged
Then y/10+3x/20=2100
Taking lcm
2y+3x=42000............2

Solving 1 and 2
X=10,000 rupees
Y=6,000 rupees