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?
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)
⇒ 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)
⇒ b + 10 = 6a – 60
⇒ 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 – 6 a + 12b = 70 + 1800
⇒ 11b = 1870
⇒ b = 170
substitute the value of b in eq 1 to get,
a – 2(170) = –300
⇒ a – 340 = –300
⇒ a = –300 + 340
⇒ a = 40
The amount of their respective capital is Rs 40 and Rs 170.
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