21. 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?
Answers
Answer:
amount of friend 1 =40 ruppees
amount of friend 2 = 170 ruppees
Step-by-step explanation:
amount of friend 1 = x
amount of friend 2 = y
x + 100 = 2(y - 100)
⇒ x + 100 = 2y - 200
⇒ x = 2y - 300
⇒x - 2y = -300 ...(1)
y + 10 = 6(x - 10)
⇒ y + 10 = 6x - 60
⇒ y = 6x - 70
⇒ 6x - y = 70 ...(2)
L.C.M of 'y' = 2,
2 (6x - y = 70)
⇒ 12x - 2y = 140 ...(3)
Solving (1) and (3),
x - 2y = -300
- (12x - 2y = 140)
⇒ x - 2y = -300
-12x + 2y = -140
⇒ -11x = -440
Therefore,
x = 40
⇒ y = 6 * 40 - 70
⇒ y = 240 - 70
= 170
Therefore,
amount of friend 1 =40 ruppees
amount of friend 2 = 170 ruppees
Let the money with first person be Rs. x and the money with the second person be Rs. y.
Then,
(x + 100) = 2(y – 100)
(y + 10) = 6(x – 10)
If first person gives Rs. 100 to second person then the second person will become twice as rich as first person. According to the given condition, we have,
(x + 100) = 2(y – 100)
x + 100 = 2y – 200
x – 2y + 100 + 200 = 0
x – 2y + 300 = 0 ——- (i)
If second person gives Rs. 10 to first person then the first person will become six times as rich as second person. According to given condition, we have
(y + 10) = 6(x – 10)
y + 10 = 6x – 60
0 = 6x – 60 – y – 10
0 = 6x – y – 70 ——- (ii)
Multiplying (ii) by 2 we get,
12x – 2y – 140 = 0 —— (iii)
By subtracting (iii) from (i), we get
-11x + 440 = 0
-11x = -440
x = 440/11 = 40
Putting x = 40 in (i) we get,
x – 2y + 300 = 0
40 – 2y + 300 = 0
-2y + 340 = 0
2y = 340
y = 340/2 = 170
Hence,
First person’s capital will be Rs. 40.
Second person’s capital will be Rs. 170.
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