Question

A person invested some amount @ 12 % simple interest and some other amount @ 10% simple interest . he recieved yearly interest 0f Rs.130. but if he interchanged the amounts invested , he would have recieved Rs.4 more as interest . how much amount did he invest at different rates?

Answer 1

12x/100 + 10y/100 = 130 ....................................eq 1
10x/100 + 12y/100 = 134.........................................eq 2
by solving we get
12x + 10y = 13000
10x + 12y = 13400
adding we get
22 ( x + y ) = 26400
x + y = 1200 .....................eq 3
subtracting we get
2 ( x - y ) = - 400
x - y = -200 ........................eq 4
on adding eq 3 and eq 4 we get
2x = 1000
x = 500
and y =1200-500
y = 700

hence the amounts are rs 500 and rs 700 respectively

Answer 2

$\huge{\boxed{\mathbb{ANSWER}}}$

Let, us suppose that :

The Person invested = Rs x at the rate of 12 percent simple interest

And

Rs y at the rate of 10 percent simple interest.

Then,    

Yearly interest = 12x/100 + 10y/100

12x/100 + 10y/100 = 130

⇒ 12x + 10y = 13000

⇒ 6x + 5y = 6500    ----- ( 1 )

√ Invested amounts interchanged, then yearly interest increases.

Therefore, 10x/100 + 12y/100 = 134

10x + 12y = 13400

5x + 6y = 6700    ------- ( 2 )

Subtract eq ( 2 ) from ( 1 ) we get :-

x-y = - 200   ---- ( 3 )

Add eq (2) and ( 1 ) we get :-

11x + 11y = 13200

⇒ x+y = 1200   ---- ( 4 )

Add eq ( 3 ) and ( 4 ) we get :-

2x = 1000

x = 500

Put x = 500 in equation ( 3 ), then we get :-

y = 700

√ Atlast, I am going to conclude my whole answer :-

• Hence, the person invested Rs 500 at the rate 12 percent  per year.

• And Rs700 at the rate of 10 percent per year.