Question

Nidhi received a simple interest rate of 1,200 when she invested ₹ x at 6% p.a. and ₹ y at 5% p.a. for 1 year. Had she invested ₹ x at 3% p.a. and ₹ y at 8% p.a. for that year, she would have received simple interest of ₹ 1,260. Find the values of x and y.

Answer 1

Nidhi received simple interest of ₹ 1200.

Interest from x at 6% = `(x xx 6 xx 1)/100`   ...`(∵ S.I. = (P xx R xx T)/100)`

= 0.06x

Interest from y at 5% = `(y xx 5 xx 1)/100`

= 0.05y

The equation is 0.06x + 0.05y = 1200

`(6x)/100 + (5y)/100 = 1200`

6x + 5y = 120000   ...(1)

The total interest from the second investment is ₹ 1260.

Interest from x at 3% = `(x xx 3 xx 1)/100`

= 0.03x

Interest from y at 8% = `(y xx 8 xx 1)/100`

= 0.08y

The equation is 0.03x + 0.08y = 1260

`(3x)/100 + (8y)/100 = 1260`

3x + 8y = 126000   ...(2)

From equation (1)

5y = 120000 – 6x

y = `(120000 - 6x)/5`  ....(3)

Substitute the value of y in equation (2)

`3x + 8 ((120000 - 6x)/5) = 126000`

`(3x)/1 + (960000 - 48x)/5 = 126000`

`(15x + 960000 - 48x)/5 = 126000`

–33x + 960000 = 630000

960000 – 630000 = 33x

330000 = 33x

x = `330000/33`

x = ₹ 10,000

Substitute the value of x in equation (3)

y = `(12000 - 6 xx 10000)/5`

= `(120000 - 60000)/5`

= `60000/5`

= 12000