Question

A man purchased 40 fruits; Apples and oranges for Rs.17. Had he purchased as manyn oranges as apples and as many apples as oranges, he would have paid Rs.15/-. Find the cost of one pair of an apple and an orange.

• A. 70 paise
• B. 60 paise
• C. 80 paise
• D. 1 rupee

Answer 1

The Correct Option is C

The problem involves solving a system of equations to find the cost of one pair of an apple and an orange.
Let's denote:
A - the number of apples purchased initially.
O - the number of oranges purchased initially.
x - the cost of one apple.
y - the cost of one orange.
P - the cost of one pair of an apple and an orange.
From the problem, we know:

• A + O = 40 (Total number of fruits)
• Ax + Oy = 17 (Total cost in rupees)
• Ox + Ay = 15 (Cost if the quantities were exchanged)

From A + O = 40, we can express A as A = 40 - O.
Substitute A in the cost equations:
(40 - O)x + Oy = 17 → 40x - Ox + Oy = 17 → 40x + (y - x)O = 17...(1)
Using the exchanged cost:
O * x + (40 - O) * y = 15 → Ox + 40y - Oy = 15 → (x - y)O + 40y = 15...(2)
We have two linear equations:

• 40x + (y - x)O = 17
• (x - y)O + 40y = 15

Add equation (1) and (2):
40x + 40y = 32
x + y = 32/40 = 0.8
So, the cost of one apple and one orange is Rs.0.80 or 80 paise.
Thus, the correct answer is 80 paise.