The cost of 4 bags and 3 boxes is ₹555 and the cost of 3 bags and 4 boxes is ₹460. What is the cost of one bag?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → ₹120
Let one bag cost ₹\(b\) and one box ₹\(x\). The two purchases give two equations; because the numbers 4 and 3 are swapped between them, adding and subtracting the equations separates \(b\) and \(x\) quickly.
\(4b+3x=555\) (1)
\(3b+4x=460\) (2)
Adding (1) and (2): \(7b+7x=1015\), so \(b+x=145\) (3)
Subtracting (2) from (1): \(b-x=95\) (4)
Adding (3) and (4), the \(x\) terms cancel: \(2b=240\), so \(b=120\)