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

(b) Rs.600

(c) Rs. 850

(d) Rs. 900

(a) Rs. 750

Let be,

**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 `\times``1/5`(10,500-8x) = 6450

⇒ 5`\times`[5x + 3 `\times``1/5`(10500-8x)] = 5`\times`6,450 (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)