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Q.

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." How much is their (each) capital?


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a

150, 40

b

40, 170

c

30, 180

d

50, 160 

answer is B.

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Detailed Solution

The first person says to the second person, "Give me a hundred, friend! I shall then become twice as rich as you."
So, let the capital of the first person be x and second be y.
Forming the linear equation from the information given above,
x+100=2(y−100)  
Rearranging and simplifying we get,
x+100=2y−200 ⇒x−2y+300=0................(1)  
Also given that the second person says to first person as, "If you give me ten, I shall be six times as rich as you."
Forming the linear equation from the information given above,
y+10=6(x−10)  
Rearranging and simplifying we get,
y+10=6x−60 ⇒6x−y−70=0...............(2)  
We make the coefficients of y equal in eq(1) and eq(2) by multiplying 2 on both the sides of equation (2).
⇒12x−2y−140=0............(3)  
By using the elimination method on eq. (1) and (2) and subtracting eq. (3) from (1) we will be finding the value of x.
⇒x−12x−2y−(−2y)+300−(−140)=0 ⇒−11x+440=0 ⇒11x=440 ⇒x=40  
By putting the value of x in eq. (1), find the value of y.
⇒40−2y+300=0 ⇒2y=340 ⇒y= 340 2 ⇒y=170  
Therefore, the money of first person and second person is 40 and 170 respectively.
Therefore, the correct option is 2.
 
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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." How much is their (each) capital?