# 8 chairs and 5 tables cost Rs.10500, while 5 chairs and 3 tables cost Rs.6450. The cost of each chair will be - Bzziii

8 chairs and 5 tables cost Rs.10500, while 5 chairs and 3 tables cost Rs.6450. The cost of each chair will be (a) Rs. 750 (b) Rs.600 (c) Rs. 850 (d)
8 chairs and 5 tables cost Rs.10500, while 5 chairs and 3 tables cost Rs.6450. The cost of each chair will be

(a) Rs. 750
(b) Rs.600
(c) Rs. 850
(d) Rs. 900

(a) Rs. 750

Explanation:
Let be,

Cost of Each Chairs = Rs x
Cost of each table = Rs y

According to the question,

Cost of 8 Chairs and 5 tables = 10,500

8x + 5y = 10,500     .....(1)

Cost of 5 Chairs and 3 tables = 6,450

5x + 3y = 6,450

From (1)

⇒ 8x + 5y = 10,500

⇒ 5y = 10500 - 8x

⇒ y = 1/5(10,500-8x)

Putting value of y in (2)

⇒ 5x + 3y = 6,450

⇒ 5x + 3 \times1/5(10,500-8x) = 6450

⇒ 5\times[5x + 3 \times1/5(10500-8x)] = 5\times6,450 (Multiply both sides by 5)

⇒ 25x + 3 (10500 - 8x) = 32250

⇒ 25x + 31500 - 24x = 32250

⇒ 25x - 24x = 32250 - 31500

⇒ x = 750

Thus,

Cost of Chair (x) = Rs. 750

So, the Correct answer is Option (a)