Question

2tables and 3chairs together cost ₹4000 whethers 3 tables and 2 chairs together cost ₹5000 then the cost of the each table and chair respectively is
a 400 and 1000
b 1000 and 400
c 1400 and 400
d 400 and 1400​

Answer 1

$\Large{\bf{\green{\mathfrak{\dag{\underline{\underline{Given:-}}}}}}}$

• 2 tables and 3 chairs together cost ₹ 4000 whereas 3 tables and 2 chairs cost ₹ 5000.

$\Large{\bf{\orange{\mathfrak{\dag{\underline{\underline{To \: Find:-}}}}}}}$

• Cost of each table and each chair

$\Large{\bf{\red{\mathfrak{\dag{\underline{\underline{Solution:-}}}}}}}$

First,

• Let number of chairs be x

• Let number of tables be y.

Now,

• 2 tables and 3 chairs together cost ₹ 4000.

Representing,

• 2y + 3x = ₹ 4000 $\longrightarrow \boxed{1}$

Second,

• 3 tables and 2 chairs cost ₹ 5000

Representing,

• 3y + 2x = ₹ 5000 $\longrightarrow \boxed{2}$

Now,

$\boxed{2} \: - \: \boxed{1}$

• 3y + 2x = ₹ 5000

• - (2y + 3x = ₹ 4000)

Continuing,

• 3y + 2x = 5000

• - 2y - 3x = - 4000

—————————————

• y - x = 1000

• y = 1000 + x $\longrightarrow \boxed{3}$

Substituting $\boxed{3}$ in $\boxed{1}$ ,

• 3y + 2x = 5000

• 3 (1000 + x) + 2x = 5000

• 3000 + 3x + 2x = 5000

• 5x = 5000 - 3000

• 5x = 2000

• x = $\sf \dfrac{2000}{5}$

• x = ₹ 400

Now,

Taking $\boxed{3}$ ,

• y = 1000 + x

• y = 1000 + 400

• y = ₹ 1400

Therefore,

• $\boxed{\pink{\textsf{Cost of each table = ₹ 1400}}}$

• $\boxed{\blue{\textsf{Cost of each chair = ₹ 400.}}}$

• $\boxed{\purple{\textsf{Option (C) ₹ 1400 and ₹ 400 is the correct option.}}}$

$\Large{\bf{\orange{\mathfrak{\dag{\underline{\underline{Verification:-}}}}}}}$

Taking $\boxed{1}$ ,

• 3y + 2x = ₹ 5000

• 3 (₹ 1400) + 2 (₹ 400) = ₹ 5000

• ₹ 4200 + ₹ 800 = ₹ 5000

• ₹ 5000 = ₹ 5000

• LHS = RHS

Taking $\boxed{2}$ ,

• 2y + 3x = ₹ 4000

• 2 (₹ 1400) + 3 (₹ 400) = ₹ 4000

• ₹ 2800 + ₹ 1200 = ₹ 4000

• ₹ 4000 = ₹ 4000

• LHS = RHS

Hence, verified.

Answer 2

Given :-

2 tables and 3 chairs together cost ₹4000 whethers 3 tables and 2 chairs together cost ₹5000

To Find :-

Cost  of the each table and chair respectively is

Solution :-

Let

Cost of chair = x

Cost of table = y

2 × x + 3 × y = 4000

2x + 3y = 4000

2x = 4000 - 3y

x = 4000 - 3y/2 (1)

3 × x + 2 × y = 5000

3x + 2y = 5000

3(4000 - 3y/2) + 2y = 5000

3 × 4000 - 3 × 3y/2 + 2y = 5000

12000 - 9y/2 + 2y = 5000

12000 - 9y + 4y = 5000 × 2

12000 - 5y = 10000

-5y = 10000 - 12000

-5y = -2000

5y = 2000

y = 2000/5

y = 400

Now

By using 1

x = 4000 - 3(400)/2

x = 4000 - 1200/2

x = 2800/2

x = 1400