Seven chairs and three tables together cost ₹ 7400, three chairs and five tables together cost ₹ 5400. The total cost (in ₹) of 1 chair and 2 tables…

Let $c$c = Cost of 1 chair (in ₹)

Let $t$t = Cost of 1 table (in ₹)

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From the given information:

Seven chairs and three tables cost ₹7400:

$7c + 3t = 7400$7c+3t=7400 ... (Equation 1)

Three chairs and five tables cost ₹5400:

$3c + 5t = 5400$3c+5t=5400 ... (Equation 2)

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To eliminate $t$t, multiply Equation 1 by 5 and Equation 2 by 3:

$35c + 15t = 37000$35c+15t=37000 ... (Equation 3)

$9c + 15t = 16200$9c+15t=16200 ... (Equation 4)

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Subtracting Equation 4 from Equation 3:

$$35c + 15t - (9c + 15t) = 37000 - 16200$$35c+15t−(9c+15t)=37000−16200

$$26c = 20800$$26c=20800

$$c = 800$$c=800

Therefore, cost of 1 chair = ₹800

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Substituting $c = 800$c=800 into Equation 1:

$$7(800) + 3t = 7400$$7(800)+3t=7400

$$5600 + 3t = 7400$$5600+3t=7400

$$3t = 1800$$3t=1800

$$t = 600$$t=600

Therefore, cost of 1 table = ₹600

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The total cost of 1 chair and 2 tables:

$$c + 2t$$c+2t

$$= 800 + 2(600)$$=800+2(600)

$$= 800 + 1200$$=800+1200

$$= 2000$$=2000

Therefore, the total cost of 1 chair and 2 tables is ₹2000.