Question

Two oranges, three bananas and four apples cost ₹ 15. Three oranges, two bananas and one apple cost ₹ 10. How much will I pay for 3 oranges, 3 bananas and 3 apples?

• A. ₹ 10
• B. ₹ 8
• C. Cannot be determined
• D. ₹ 15

Hint:

In linear system word problems, sometimes the exact values are not needed. Combine equations cleverly to form the target expression directly.

Answer 1

The Correct Option is D

Step 1: Define variables and form equations
Let orange \(=O\), banana \(=B\), apple \(=A\).
Equation (1): \(2O+3B+4A=15\).
Equation (2): \(3O+2B+A=10\).
Step 2: Determine the target expression
We aim to find \(3O+3B+3A\).
Step 3: Manipulate equations to find the target expression
Multiply equation (2) by 3: \(9O+6B+3A=30\).
Multiply equation (1) by 3: \(6O+9B+12A=45\).
Subtract the second modified equation from the first: \((9O-6O)+(6B-9B)+(3A-12A)=30-45\).
\(⇒ 3O-3B-9A=-15\ \(⇒\) O-B-3A=-5\).
Add equations (1) and (2): \((2O+3O)+(3B+2B)+(4A+A)=15+10\).
\(⇒ 5O+5B+5A=25 \(⇒\) O+B+A=5\).
Therefore \(3O+3B+3A=15\).
\[ \boxed{₹ 15} \]