A and B each have a certain number of mangoes. A says to B, "if you give 30 of your mangoes, I will have twice as many as left with you." B replies, "if you give me 10, I will have thrice as many as left with you." How many mangoes does each have?
Answers
Given : A and B each have a certain number of mangoes. A says to B, "if you give 30 of your mangoes, I will have twice as many as left with you." B replies, "if you give me 10, I will have thrice as many as left with you."
Solution:
Let A has mangoes = x and B has mangoes = y
ATQ :
Condition: 1
(x + 30) = 2(y - 30)
(x + 30) = 2y - 60
x = 2y - 60 - 30
x = 2y - 90…………....(1)
Condition: 2
3(x - 10) = (y + 10)
3x - 30 = (y + 10)
3x = y + 10 + 30
3x = y + 40…………... (2)
On putting the value of x from eq (1) in eq (2) we obtain :
3(2y - 90) = y + 40
6y - 180 = y + 40
6y - y = 40 + 180
5y = 310
y = 310/5
y = 62
On putting the value of y in eq (1) we obtain :
x = 2y - 90
x = 2 × 62 - 90
x = 124 - 90
x = 34
Hence A has 34 mangoes and B has 62 mangoes.
Hope this answer will help you…
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