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A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby, getting a sum Rs 1008. If she had sold the saree at 10% profit and the sweater at 8% discount, she would have got Rs 1028. Find the cost price of the saree and the list price (price before discount) of the sweater

Solution:

Consider ₹x as the cost price of the saree

Consider ₹y as the list price of the sweater

Case I :

Selling a saree at 8% profit + Selling a sweater at 10% discount = ₹1008

It can be written as

(100 + 8)% of x + (100 - 10)% of y = 1008

So we get

108% of x+ 90% of y = 1008

1.08x + 0.9 y = 1008--------------(1)

Case II:

Sold the saree at 10% profit + Sold the sweater at 8% discount = ₹1028

It can be written as

(100 + 10)% of x + (100 - 8)% of y = 1028

So we get

110% of x + 92% of y = 1028

1.1x + 0.92y = 1028----------------(2)

Solve the linear equations (1) and (2)

Substitute the value of y from (1),in (2),we get,

1.1 x 0.92( 1008-1.08x/0.9)

1.1 x 0.9x + 927.36 - 0.9936x = 1028 x 0.9

0.99x - 0.9936x = 925.2 - 927.36

-0.0036x =-2.16

x = 2.16/0.0036

x = 600.

Substituting the value of x in (1),we get,

1.08 x 600+ 0.9y= 1008

648 + 0.9y = 1008

0.9y = 1008 - 648

0.9y = 360

y = 360/0.9

y = 400.

So we get

x = 600.

y = 400.

Therefore, the cost price of the saree and the list price (price before discount) of the sweater are ₹600 and ₹400, respectively.

✦ Try This: A shopkeeper sells a saree at 10% profit and a sweater at 12% discount, thereby, getting a sum of Rs 1000. If she had sold the saree at 12% profit and the sweater at 10% discount, she would have got Rs 1008. Find the cost price of the saree and the list price (price before discount) of the sweater

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3

NCERT Exemplar Class 10 Maths Exercise 3.4 Problem 11

A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby, getting a sum Rs 1008. If she had sold the saree at 10% profit and the sweater at 8% discount, she would have got Rs 1028. Find the cost price of the saree and the list price (price before discount) of the sweater

Summary:

A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby, getting a sum Rs 1008. If she had sold the saree at 10% profit and the sweater at 8% discount, she would have got Rs 1028. The cost price of the saree and the list price (price before discount) of the sweater are ₹600 and ₹400, respectively.

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