Shortcut Trick
Equate the two scenarios since the total money spent is the same: 2 Sarees + 4 Shirts = 1 Saree + 6 Shirts.
Subtracting 1 Saree and 4 Shirts from both sides: 1 Saree = 2 Shirts.
Substitute 1 Saree in the second condition: (2 Shirts) + 6 Shirts = 8 Shirts = ₹1,600.
Since 8 Shirts cost ₹1,600, then 1 Shirt costs ₹200.
Cost for 12 Shirts = 12 × ₹200 = ₹2,400.
∴ The correct answer is ₹2,400.
Alternate Method
Given:
Cost of 2 Sarees (S) + 4 Shirts (H) = ₹1,600
Cost of 1 Saree (S) + 6 Shirts (H) = ₹1,600
Calculations:
⇒ Let S be the price of one Saree and H be the price of one Shirt.
⇒ 2S + 4H = 1,600 --- (i)
⇒ 1S + 6H = 1,600 --- (ii)
⇒ Multiply equation (ii) by 2: 2S + 12H = 3,200 --- (iii)
⇒ Subtract equation (i) from (iii): (2S + 12H) − (2S + 4H) = 3,200 − 1,600
⇒ 8H = 1,600
⇒ H = 1,600 ÷ 8 = 200
⇒ Required amount for 12 Shirts = 12 × H
⇒ 12 × 200 = ₹2,400
∴ The correct answer is ₹2,400.
Additional Information
Linear Equations in Two Variables
Equations in the form ax + by = c can be solved using substitution, elimination, or cross-multiplication methods.
Substitution Method
Expressing one variable in terms of the other from one equation and substituting it into the second equation to find the value of the variables.
Simultaneous Equations
A set of equations that are satisfied by the same values of the variables; finding these values is known as solving the system.