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Natu and Buchku each have 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 as left with you”. What is the number of oranges with Natu and Buchku, respectively ?
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- 50, 20
- 70, 50
- 20, 50
- 50, 70
Correct Option: B
Let the number of oranges with Natu be x.
Number of oranges with Buchku = y
Case I,
x + 10 = 2 (y – 10)
⇒ x + 10 = 2y – 20
⇒ 2y – x = 20 + 10 = 30 ..(i)
Case II,
y + 10 = x – 10
⇒ x – y = 10 + 10 = 20 ... (ii)
On adding equations (i) and (ii),
2y – x + x – y = 30 + 20
⇒ y = 50
From equation (ii),
x – 50 = 20
⇒ x = 50 + 20 = 70
