Question

The price of 12 chairs and 8 tables is Rs. 676. What is the price of 21 chairs and 14 tables?
(a) Rs. 1183
(b) Rs. 4732
(c) Rs. 1180
(d) Cannot be determined

Answer 1

Hint: We will solve this question by taking x as the price of one chair and y as the price of one table. Now as per given in question we will write the relation between x and y and then we will try to multiply or divide it by some number to get the desired value.

Complete step-by-step answer:
Let, x = price of one chair
y= price of one table
Now as per given in the question we will write the relation,
12x + 8y = 676
Now we will try to convert it in the form of 21x + 14y by multiplying and dividing by some integer, and if it cannot be converted then the answer will be unable to be determined.
$\begin{align}
  & 12x+8y=676 \\
 & \Rightarrow 4\left( 3x+2y \right)=676 \\
 & \Rightarrow 3x+2y=169 \\
\end{align}$
Now we can multiply both the sides by 7 to get 21x + 14y,
Therefore,
$21x+14y=169\times 7=1183$
Hence the correct answer is 1183, which is option (a).

Note: While solving this question student might make a mistake thinking that they need two equations to solve this question and will mark option (d) as correct answer, but before marking that one should always check that if the two equations are parallel or not, and in this case it was parallel so we can solve this question with just one equation only as the required one will be the integral multiple of the given equation.