Question

the total cost of a pant and a shirt is rs 490.. if the cost of the shirt is 30 % more than one third of the cost of the pant .find the cost of each

Answer 1

GIVEN :-

• The total cost of a pant and a shirt is Rs.490.
• the cost of shirt is 30% more than one third of the cost of pant.

TO FIND :-

• the cost of each.

SOLUTION :-

Let the cost of pant be x.

A.T.Q

⇒ x + 30% of x + 1/3 × x = 490

⇒ x + 30/100 × x + x/3 = 490

⇒ x + 30x/100 + x/3 = 490

⇒ (100x + 30x)/100 + x/3 = 490

⇒ 130x/100 + x/3 = 490

⇒ 390x/300 + 100x/300 = 490

⇒ (390x + 100x)/300 = 490

⇒ 490x/300 = 490

⇒ x = (490 × 300)/490

⇒ x = 300

Hence cost of pant = x = Rs.300

Cost of shirt = 30% of x + 1/3 × x

= 30/100 × 300 + 1/3 × 300

= 30 × 3 + 100

= 190

Hence cost of shirt = Rs.190

VERIFICATION :-

⇒ Total cost = cost (shirt) + cost (pant)

⇒ 490 = 190 + 300

⇒ 490 = 490

L.H.S = R.H.S

HENCE VERIFIED

Answer 2

Question:

The total cost of a pant and a shirt is ₹ 490. If the cost of the shirt is 30 % more than one third of the cost of the pant . Find the cost of each.

To find:

• Cost of shirt

• Cost of pant

Answer:

$\bigstar The \: cost \: of \: pant \: is \: \sf \red{\bold{Rs\: 300}}.$

$\bigstar The \: cost \: of \: shirt \: is \: \sf \red{\bold{Rs\: 190}}.$

Given:

• The total cost of a pant and a shirt is ₹ 490

• the cost of the shirt is 30 % more than one third of the cost of the pant

Step-by-step explanation:

$\implies x + 30\% \times x + \frac{1}{3} \times x = 490$

$\implies x + \frac{30}{100}x + \frac{x}{3} = 490$

L.C.M. is 300

$\implies \frac{300x + 90x + 100x}{300} = 490$

$\implies 300x + 90x + 100x = 490(300)$

$\implies 490x = 490(300)$

$\implies \boxed{x = 300}$

$\therefore The \: cost \: of \: pant \: is \: \sf \pink{\bold{Rs\: 300}}.$

$Cost \: of \: shirt = 30\%x + \frac{1}{3} x$

$= \frac{30}{100} \times 300 + \frac{1}{3} \times 300$

$= 90 + 100$

$\therefore The \: cost \: of \: shirt \: is \: \sf \pink{\bold{Rs\: 190}}.$

Hint given in the question :

★ The total cost of a pant and a shirt is ₹ 490

★ the cost of the shirt is 30 % more than one third of the cost of the pant .

⚠️ Note ⚠️

Read carefully the hint.

Verification:

$\boxed{Total \: cost = cost \: of \: shirt + cost \: of \:pant}$

$490 = 190 + 300$

$\boxed{490 = 490}$

$Hence \: verified.$