The cost of 5 kg of apples and 3 kg of oranges is ₹535. If the cost of 8 kg of apples and 6 kg of oranges is ₹910, then what is the cost of 2 kg of apples and 8 kg of oranges?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → ₹520
Let one kg of apples cost ₹\(a\) and one kg of oranges ₹\(b\). The two given costs give two equations, and the orange terms cancel once the first equation is doubled.
\(5a+3b=535\) (1)
\(8a+6b=910\) (2)
Doubling (1): \(10a+6b=1070\) (3)
Subtracting (2) from (3), the \(b\) terms cancel: \(2a=160\), so \(a=80\)
From (1): \(3b=535-400=135\), so \(b=45\)
Cost of 2 kg of apples and 8 kg of oranges:
\(2a+8b=160+360=520\)