Question

The total price of 8 chairs and 5 tables is
Rs. 92 and total price of 5 chairs and 8
tables is Rs. 77. What is the difference
between the price of 1 table and 1 chair?
(1) Rs. 9 (2) Rs. 5 (3) Rs. 8
(4) Rs. 13
(5) 7​

Answer 1

Step-by-step explanation:

Given:-

• The total cost of 8 chairs and 5 tables is Rs.92

• The total cost of 5 chairs and 8 tables is Rs.77

To Find:-

• The difference between the price of 1 table and 1 chair.

Solution:-

Let the cost of a chair be x

And the cost of a table be y

Condition 1:-

The total cost of 8 chairs and 5 tables is Rs.92

$\sf \implies 8x + 5y = 92.....(i)$

Condition 2:-

The total cost of 5 chairs and 8 tables is Rs.77

$\sf \implies 5x + 8y = 77.....(ii)$

Adding (i) and (ii)

$\sf \implies 8x + 5y + 5x + 8y = 92 + 77$

$\sf \implies 13x + 13y = 169.....(iii)$

Equation (i) - (ii)

$\sf \implies x + y = 13.....(iii)$

$\sf \implies 8x + 5y - 5x - 8y = 92 - 77$

$\sf \implies 3x - 3y = 15$

$\sf \implies x - y = 5......(iv)$

Adding (iii) and (iv):-

$\sf \implies x + y + x - y = 13 + 5$

$\sf \implies 2x = 18$

$\sf \implies x = 9$

Substitute x = 8 in equation (iii)

$\sf \implies x + y = 13$

$\sf \implies 9 + y = 13$

$\sf \implies y = 4$

Cost of 1 chair = Rs.9

Cost of 1 table = Rs.4

The difference between the price of 1 table and 1 chair

= x - y

= 9 - 4

= Rs.5

Option (2)

Answer 2

Given

• The total price of 8 chairs and 5 tables is Rs. 92

• total price of 5 chairs and 8tables is Rs. 77.

To Find-

• difference between the price of 1 table and 1 chair

Consept used-

• Elimination method

Solution-

Let the price of 1 chair be x

and the price of 1table be y

In 1st condition

Given that

The total price of 8 chairs and 5 tables is Rs. 92

$\therefore \rm \boxed{ \rm8x + 5y = 92}......1$

In 2nd condition

Given that

total price of 5 chairs and 8 tables is Rs. 77.

$\therefore \boxed{ \rm \: 5x + 8y = 77}......2$

By elimination method

We have to find the value of x and y so the best way to solve this is elimination method where we eliminate 1term(x or y) and solve the second term

So we multiply 5 in first equation and 8 in second equation

$\rm 40x + 25y = 460 \\ \\ \rm \boxed{ \tiny{ - }} 40x + 64y = 616 \\ \underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \rm { - 39 y= - 156} \\ \\ \underline{ \boxed{ \bf \: y = 4}}$

Hence the price of one table is Rs4

Now we find the value of x by putting the value of y in 1st equation

$\rm \: 8x + 5 \times 4 = 92 \\ \\ \implies \rm8x = 92 - 20 \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \rm \: x = \frac{72}{8} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \rm \underline{ \boxed{ \bf \: x = 9}}$

Hence the price of one chair is Rs9

Now we find the difference between price of 1 chair and 1table

$\therefore \rm difference \: between \: price \: of \: 1chair \: and \: 1 \: table = x - y \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \rm \: 9 - 4 = 5$

Hence the difference between price of one chair and one table is Rs5

Hence option 2nd is correct