Question

The cost of 5 oranges and 3 apples is Rs. 35 and the cost of 2 oranges and 4 apples is Rs. 28. What would be the cost of one each of orange and apple?

• A. Orange Rs. 4, Apple Rs. 5
• B. Orange Re. 1, Apple Rs. 10
• C. Orange Rs. 2, Apple Rs. 4
• D. Orange Rs. 4, Apple Rs. 6

Hint:

Trial and error with the options is often faster for such simple linear equations!

Answer 1

The Correct Option is A

Step 1: Concept
Set up a system of linear equations. Let cost of orange = $x$ and apple = $y$.

Step 2: Analysis
Eq 1: $5x + 3y = 35$
Eq 2: $2x + 4y = 28 \Rightarrow x + 2y = 14$.

Step 3: Reasoning
From Eq 2: $x = 14 - 2y$. Substitute into Eq 1:
$5(14 - 2y) + 3y = 35$
$70 - 10y + 3y = 35$
$35 = 7y \Rightarrow y = 5$. If $y = 5$, then $x = 14 - 10 = 4$.

Step 4: Conclusion
Orange cost = Rs. 4, Apple cost = Rs. 5. Final Answer: (A)