Question

If cost of 4 chairs and 7 tables is Rs. 360 and cost of 6 chairs and 10 tables is Rs. 520, then find the cost of one chair and one table separately.

Hint:

To solve linear equations with two variables, align coefficients and use elimination or substitution method for quick results.

Answer 1

Step 1: Let the cost of one chair be Rs. x and one table be Rs. y. 
Step 2: Form the equations from the given information. 
\[ 4x + 7y = 360 \quad \text{...(1)} \] \[ 6x + 10y = 520 \quad \text{...(2)} \] Step 3: Simplify the equations. 
Divide equation (2) by 2: \[ 3x + 5y = 260 \quad \text{...(3)} \] Now we have: (1) $4x + 7y = 360$ (3) $3x + 5y = 260$ 
Step 4: Eliminate one variable. 
Multiply (3) by 4 and (1) by 3 to make the coefficients of $x$ equal: \[ 12x + 20y = 1040 \quad \text{...(4)} \] \[ 12x + 21y = 1080 \quad \text{...(5)} \] 
Step 5: Subtract equation (4) from (5). 
\[ (12x + 21y) - (12x + 20y) = 1080 - 1040 \] \[ y = 40 \] 
Step 6: Substitute $y = 40$ in equation (3). 
\[ 3x + 5(40) = 260 \Rightarrow 3x + 200 = 260 \Rightarrow 3x = 60 \Rightarrow x = 20 \] Step 7: Conclusion. 
\[ \boxed{\text{Cost of one chair} = Rs.\,20, \quad \text{Cost of one table} = Rs.\,40} \]