Question

One says, "give me 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

Let the capitals be ‘a’ and ‘b’.

Given, one says, “give me hundred, friend! I shall then become twice as rich as you” .

Lets assume "b" gives hundred to "a".According to given condition

$a+100=2(b–100)\Rightarrow a+100=2b–200$

$a=2b-200–100$

$a=2b–300$

$a-2b=-300$------ (1)

Now The other replies, “If you give me ten, I shall be six times as rich as you.”

Which means "a" gives 10 to "b".

So,

$b+10=6(a–10)\Rightarrow b+10=6a–60\Rightarrow b=6a–60–10$

$b=6a–70$

$6a-b=70$ ----- (2)

Multiplying eq1 by 6 and subtract from eq2

$6a-b-6(a-2b)=70-6(-300)$

$6a-b-6a+12b=70+1800$

$11b=1870$

$b=170$

substitute the value of b in eq 1 to get,

$a-2\left(170\right)=-300$

$a-340=-300$

$a=-300+340$

$a=40$

The amount of their respective capital is Rs 40 and Rs 170.