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The cost of 5 shirts and 3 t-shirts is ₹2500 and the cost of 2 shirts and 4 t-shirts is ₹1400. Find the cost of a shirt and a t-shirt respectively.

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The cost of a shirt and a t-shirt are ₹414.29 and ₹142.85 respectively

The cost of a shirt and a t-shirt are ₹404.29 and ₹140.85 respectively

The cost of a shirt and a t-shirt are ₹400.29 and ₹132.85 respectively

The cost of a shirt and a t-shirt are ₹420.29 and ₹142.85 respectively

answer is A.

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Detailed Solution

It is given that the cost 5 shirts and 3 t-shirts is ₹2500.
The cost of 2 shirts and 4 t-shirts is ₹1400.
Suppose the cost a shirt and a t-shirt be x and y respectively.

⇒ 5 x + 3 y = 2500 ⇒ 2 x + 4 y = 1400

The solution of the equations

a_{1} x + b_{1} y + c_{1} = 0 and a_{2} x + b_{2} y + c_{1} = 0

by cross multiplication method is given by the formula,

\frac{x}{b_{1} c_{2} - b_{2} c_{1}} = \frac{y}{a_{2} c_{1} - a_{1} c_{2}} = \frac{1}{a_{1} b_{2} - a_{2} b_{1}}

Here

a 1 = 5, b 1 = 3, c 1 = − 2500, a 2 = 2, b 2 = 4, c 2 = − 1400

.
Using the cross-multiplication method to find the value of x and y,

⇒ x 3 − 1400 − 4 − 2500 = y − 25002 − (− 1400) 5 = 1 5 (4) − 2 (3) ⇒ x − 4200 + 10000 = y − 5000 + 7000 = 1 20 − 6 ⇒ x 5800 = y 2000 = 114

Solving the above expression for x and y,

⇒ x 5800 = 114 ⇒ x = 414.29 A n d, ⇒ y 2000 = 114 ⇒ y = 142.85

The cost of a shirt and a t-shirt are ₹414.29 and ₹142.85 respectively.
Hence, option 1 is correct.

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