The cost of 5 shirts and 7 trousers together is ₹6,150 and the cost of 3 shirts is equal to the cost of 4 trousers. What is the cost (in ₹) of 2 shirts and 2 trousers together?​

Correct option is C

​Given:

The cost of 5 shirts and 7 trousers together is ₹6,150.

The cost of 3 shirts is equal to the cost of 4 trousers.

Solution:

Let the cost of one shirt be S and the cost of one trouser be T

From the given information:

Equation 1: 5S + 7T = 6150

Equation 2:  3S = 4T,

S = $$\frac{4T}{3}$$​​

Substituting S = $$\frac{4T}{3}$$​ into Equation 1:

$$5\left(\frac{4T}{3}\right) + 7T = 6150$$​​

​$$\frac{20T}{3} + 7T = 6150$$​​

​$$\frac{20T + 21T}{3} = 6150$$​​

​$$\frac{41T}{3} = 6150$$​​

​$$41T = 6150 \times 3 = 18450$$​​

T = $$\frac{18450}{41}$$​ = 450

Substituting T = 450 back into Equation 2 :

3S = $$4 \times 450$$​ = 1800

S = $$\frac{1800}{3}$$​ = 600

The cost of 2 shirts and 2 trousers together is:

2S + 2T = 2 × 600 + 2 × 450 = 1200 + 900 = 2100

Thus, the cost of 2 shirts and 2 trousers together is ₹2,100