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?
Answers
Given : 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."
Solution:
Let one friend has capital amount = ₹ x and other friend has capital amount = ₹ y .
ATQ :
Condition: 1
x + 100 = 2(y − 100)
x + 100 = 2y − 200
x - 2y = -200 -100
x − 2y = - 300……………….(1)
Condition: 2
6(x − 10) = (y + 10)
6x − 60 = y + 10
6x - y = 10 +60
6x − y = 70…………………….(2)
By using the elimination method :
On Multiplying equ (2) by 2 :
12x − 2y = 140……………….(3)
On Subtracting equation (1) from equation (3) :
12x − 2y - (x − 2y ) = 140 - (- 300)
12x - 2y - x + 2y = 140 + 300
11x = 140 + 300
11x = 440
x = 440/11
x = 40
On putting x = 40 in equation (1) :
x − 2y = −300
40 − 2y = −300
40 + 300 = 2y
2y = 340
y = 340/2
y = 170
Hence, the amount of first friend capital is ₹ 40 and the amount of second friend capital is ₹ 170.
Hope this answer will help you…
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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.