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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”. Tell me what is the amount of their respective capital?

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Rs . 70 and Rs . 160

Rs . 66 and Rs . 190

Rs . 40 and Rs . 170

Rs . 30 and Rs . 120

answer is C.

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Detailed Solution

Given two friends.
Let one has x Rs. and others has y Rs.,
Then according to the question,

\Rightarrow (x + 100) = 2 (y - 100)

\Rightarrow x + 100 = 2 y - 200

\Rightarrow x - 2 y = - 300

………(1)
Also,

6 (x - 10) = y + 10

\Rightarrow 6 x - 60 = y + 10

\Rightarrow 6 x - y = 70

………..(2)
Multiply equation (2) by 2,

\Rightarrow 12 x - 2 y = 140

………….(3)
Subtract equation (1) and equation (3),

\Rightarrow - 11 x = - 440

\Rightarrow x = 40

Substituting

x = 40

in equation (1),

\Rightarrow 40 - 2 y = - 300

\Rightarrow - 2 y = - 340

\Rightarrow y = 170

One has 40 Rs and others has 170 Rs.
Therefore, option (3) is correct.

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