Question

12. One says, “Give me a hundred, friend! I shall then become twice as rich as you." The other replies, "If you give me ten, I shall be six times as rich as you." Tell me what is the amount of their respective capital? ​

Answer 1

Answer:

Then according to the question:

x+100=2(y−100)

x+100=2y−200

x−2y=−300…(1)

And,

6(x−10)=(y+10)

6x−60=y+10

6x−y=70…(2)

Multiplying equation (2) by 2, we get:

12x−2y=140…(3)

Subtracting equation (1) from equation (3), we get:

11x=140+300

11x=440

x=40

Substitute the vale of x in equation (1), we get:

40−2y=−300

40+300=2y

2y=340

y=

2

340

=170

∴ The friends had Rs. 40 and Rs. 170 with them respectively.

Answer 2

$\large\underline{\sf{Solution-}}$

Let assume that,

Amount of first person be Rs x

and

Amount of second person be Rs y

According to statement,

First person said to second person, “Give me a hundred, friend! I shall then become twice as rich as you."

Thus,

Amount of first person be Rs x + 100

and

Amount of second person be Rs y - 100

So,

$\rm :\longmapsto\:x + 100 = 2(y - 100)$

$\rm :\longmapsto\:x + 100 = 2y - 200$

$\bf\implies \:x - 2y = - \: 300 - - - (1)$

According to second condition

Second person said to first person, "If you give me ten, I shall be six times as rich as you."

Thus,

Amount of first person be Rs x - 10

and

Amount of second person be Rs y + 10

So,

$\rm :\longmapsto\:y + 10 = 6(x - 10)$

$\rm :\longmapsto\:y + 10 = 6x - 60$

$\bf\implies \:6x - y = 70 - - - - (2)$

Now, we have two linear equations.

$\bf\implies \:x - 2y = - 300- - - - (1)$

and

$\bf\implies \:6x - y = 70 - - - - (2)$

can be rewritten as

$\rm :\longmapsto\:12x - 2y = 140 - - - (3)$

On Subtracting equation (1) from equation (2), we get

$\rm :\longmapsto\:11x = 440$

$\bf\implies \:x = 40$

On substituting x = 40, in equation (1), we get

$\rm :\longmapsto\:40 - 2y = - 300$

$\rm :\longmapsto\: - 2y = - 300 - 40$

$\rm :\longmapsto\: - 2y = - 340$

$\bf\implies \:y = 170$

Therefore,

Amount of first person be Rs 40

and

Amount of second person be Rs 170