Finding Cost Price and Marked Price

Video Explanation

Question

A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, getting ₹1008. If she sold the saree at 10% profit and the sweater at 8% discount, she would get ₹1028. Find the cost price of the saree and the list price of the sweater.

Solution

Step 1: Let Variables

Let cost price of saree = \(x\)

Let list price of sweater = \(y\)

—

Step 2: Form Equations

First condition:

Saree sold at 8% profit → \(1.08x\)

Sweater sold at 10% discount → \(0.9y\)

\[ 1.08x + 0.9y = 1008 \quad (1) \]

— Second condition:

Saree at 10% profit → \(1.1x\)

Sweater at 8% discount → \(0.92y\)

\[ 1.1x + 0.92y = 1028 \quad (2) \]

—

Step 3: Remove Decimals

Multiply (1) by 100:

\[ 108x + 90y = 100800 \quad (3) \]

Multiply (2) by 100:

\[ 110x + 92y = 102800 \quad (4) \]

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Step 4: Solve Linear Equations

Multiply (3) by 92:

\[ 9936x + 8280y = 9273600 \quad (5) \]

Multiply (4) by 90:

\[ 9900x + 8280y = 9252000 \quad (6) \]

Subtract (6) from (5):

\[ 36x = 21600 \]

\[ x = 600 \]

Substitute into (3):

\[ 108(600) + 90y = 100800 \]

\[ 64800 + 90y = 100800 \]

\[ 90y = 36000 \Rightarrow y = 400 \]

—

Conclusion

\[ \text{Cost price of saree} = ₹600,\quad \text{List price of sweater} = ₹400 \]

Verification

Check 1: \(648 + 360 = 1008\) ✔

Check 2: \(660 + 368 = 1028\) ✔