Question

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? [From the Bijaganita of Bhaskara II]
[Hint : x + 100 = 2(y – 100), y + 10 = 6(x – 10)].

NCERT Class X
Mathematics - Mathematics

Chapter _PAIR OF LINEAR EQUATIONS
IN TWO VARIABLES

Answer 1

a/q x+100=2y-200
 x=2y-300
x-2y=-300
and   y+10=6x-60
        y-6x=-70
therefore, multiplying first equation by 1 and 2nd equation by 2
now, x-2y=-300 
   -12x+2y=-140
on adding both equation
     -11x=-440
         x=40 answer
now 40-2y=-300
       -2y=-340
          y=170 answer

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the initial amount be Rs x

And with other one be Rs y .

According to the Question,

1st Part

⇒ x + 100 = 2(y - 100)

⇒ x + 100 = 2y - 200

⇒ x - 2y = - 300 ..... (i)

2nd Part

⇒ 6(x - 10) = (y + 10)

⇒ 6x - 60 = y + 10

⇒ 6x - y = 70.... (ii)

Solving Eq (i) and (ii), we get

⇒ 11x = 140 + 300

⇒ 11x = 440

⇒ x = 40

Putting x's value in Eq (i), we get

⇒ 40 - 2y = - 300

⇒ 40 + 300 = 2y

⇒ 2y = 340

⇒ y = 340/2

⇒ y = 170

Hence, the amount of their respective capital are Rs. 40 and Rs. 170.