Question : Natu and Buchku each have a certain number of oranges. Natu says to Buchku, "If you give me 10 of your oranges, I will have twice the number of oranges left with you". Buchku replies, "If you give me 10 of your oranges, I will have the same number of oranges left with you". What is the number of oranges with Natu and Buchku respectively?
Option 1: 50, 20
Option 2: 70, 50
Option 3: 20, 50
Option 4: 50, 70
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Correct Answer: 70, 50
Solution :
Let the number of oranges with Buchku = $y$
And the number of oranges with Natu = $x$
When Buchku gives oranges:
$x + 10 = 2(y -10)$
⇒ $x +10 = 2y -20$
⇒ $x - 2y = -30$ (equation 1)
When Natu gives oranges:
$y + 10 = x -10$
⇒ $x - y = 20$
⇒ $x = 20 + y$ (equation 2)
Putting the value of $x$ in equation 1, we get,
$20 + y - 2y = -30$
⇒ $-y = -50$
$\therefore y = 50$
Putting the value of $y$ in equation 1, we get,
$x – 2×50 = -30$
⇒ $x = -30 + 100$
$\therefore x = 70$
Hence, the correct answer is (70, 50).
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