Math, asked by roxykennedy1995, 11 months ago

A person invested some amount at the rate of 10% simple interest and some other amount at the rate of 12% simple interest . He received yearly interest of rs 130 . But if he had interchanged the amount invested he would have received rs 4 more as interest how much amount did he invest at different rates

Answers

Answered by gauravdevnani04

Let the amount that is invested ..be rupees x at rate of 12% and rupees y at rate of 10%.

NOW , ACCORDING TO QUESTION, WE HAVE

Simple interest on rupees x at 12% + Simple interest on rupees y at 10% =130

SINCE, SIMPLE INTEREST = ( principle × rate × time ) /100

(x × 12 × 1 ) /100 + ( y × 10 × 1 ) /100 = 130

12x + 13y = 13000 ( 1st equation )

AS HE HAVE INTERCHANGED THE AMOUNT INVESTED, he would have received 4 more on interest.

then, another equation will be :-

(x × 10 × 1) /100 + (y × 12 ×1) /100 = 130+4 = 134

therefore, 10x + 12y = 13400 ( 2nd equation )

MULTIPLYING EQUATION 1 BY 12 AND EQUATION 2 BY 10, WE GET

144x + 120y = 156000

100x + 120y = 134000

SUBTRACTING BOTH EQUATIONS, WE GET

x = 500

PUTTING VALUE OF X IN EQUATION 1 , we get

12 × 500 +10y = 13000

6000 + 10y = 13000

10y = 7000

y = 700

HENCE , AMOUNT INVESTED AT 12% IS 500 AND AMOUNT INVESTED AT 10% IS 700.

USING SIMPLE INTEREST FORMULA SI = ( P × R × T ) /100, we get

value of x = rupees 500

value of y = rupees 700

Answered by shashankm3445

Answer:

value of x = rupees 500

value of y = rupees 700

Step-by-step explanation:

Let the amount that is invested ..be rupees x at rate of 12% and rupees y at rate of 10%.

NOW , ACCORDING TO QUESTION, WE HAVE

Simple interest on rupees x at 12% + Simple interest on rupees y at 10% =130

SINCE, SIMPLE INTEREST = ( principle × rate × time ) /100

(x × 12 × 1 ) /100 + ( y × 10 × 1 ) /100 = 130

12x + 13y = 13000 ( 1st equation )

AS HE HAVE INTERCHANGED THE AMOUNT INVESTED, he would have received 4 more on interest.

then, another equation will be :-

(x × 10 × 1) /100 + (y × 12 ×1) /100 = 130+4 = 134

therefore, 10x + 12y = 13400 ( 2nd equation )

MULTIPLYING EQUATION 1 BY 12 AND EQUATION 2 BY 10, WE GET

144x + 120y = 156000

100x + 120y = 134000

SUBTRACTING BOTH EQUATIONS, WE GET

x = 500

PUTTING VALUE OF X IN EQUATION 1 , we get

12 × 500 +10y = 13000

6000 + 10y = 13000

10y = 7000

y = 700

HENCE , AMOUNT INVESTED AT 12% IS 500 AND AMOUNT INVESTED AT 10% IS 700.

USING SIMPLE INTEREST FORMULA SI = ( P × R × T ) /100, we get

value of x = rupees 500

value of y = rupees 700

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