The price of 2 sarees and 4 shirts is Rs. 1600. With the same money, one can buy 1 saree and 6 shirts. How much is payable for 12 shirts?

Given data

• 2 sarees + 4 shirts = Rs. 1600.
• 1 saree + 6 shirts = Rs. 1600.

Concept / Approach

• Let saree price = a, shirt price = b. Form two linear equations and solve.

Step-by-step calculation

2a + 4b = 1600 … (1)a + 6b = 1600 … (2)From (2): a = 1600 − 6b.Substitute in (1): 2(1600 − 6b) + 4b = 1600 ⇒ 3200 − 12b + 4b = 1600 ⇒ −8b = −1600 ⇒ b = 200.Then a = 1600 − 6×200 = 400.Cost of 12 shirts = 12 × 200 = Rs. 2400.

Verification

Check (1): 2×400 + 4×200 = 800 + 800 = 1600 ✔; (2): 400 + 1200 = 1600 ✔.

Common pitfalls

• Mis-eliminating variables or arithmetic slips while substituting.

Final Answer

Rs. 2400.