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A TV set is being sold for ₹ X in Delhi....

A TV set is being sold for ₹ X in Delhi. A dealer went to Chandigarh and bougth the TV at 20% discount (from the price of Delhi). He spent ₹ 600 on transport. Thus he sold the set in Delhi for ₹ X making `((100)/(7))%` profit What is the value of X?
(a)₹ 7200
(b)₹ 8000
(c)₹ 8800
(d)₹ 9600

A

₹ 7200

B

₹ 8000

C

₹ 8800

D

₹ 9600

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we will break down the information given and use it to find the value of \( X \). ### Step 1: Understand the Problem The TV is sold for \( ₹ X \) in Delhi. The dealer buys the TV in Chandigarh at a 20% discount on the price in Delhi and incurs a transport cost of ₹ 600. He then sells the TV in Delhi for \( ₹ X \) and makes a profit of \( \frac{100}{7}\% \). ### Step 2: Calculate the Cost Price (CP) The dealer buys the TV at a 20% discount. This means he pays 80% of the price in Delhi. \[ \text{CP} = X \times \frac{80}{100} = \frac{4X}{5} \] ### Step 3: Add Transport Cost to Cost Price The dealer also spends ₹ 600 on transport. Therefore, the total cost price (including transport) becomes: \[ \text{Total CP} = \frac{4X}{5} + 600 \] ### Step 4: Calculate Selling Price (SP) with Profit The dealer sells the TV for \( ₹ X \) and makes a profit of \( \frac{100}{7}\% \). To express this profit as a fraction: \[ \frac{100}{7}\% = \frac{100}{700} = \frac{1}{7} \] This means the selling price is \( \frac{8}{7} \) of the cost price. Therefore, we can set up the equation: \[ X = \frac{8}{7} \times \text{Total CP} \] ### Step 5: Substitute Total CP into the Equation Substituting the expression for Total CP into the equation gives: \[ X = \frac{8}{7} \left( \frac{4X}{5} + 600 \right) \] ### Step 6: Clear the Fraction To eliminate the fraction, multiply both sides by 7: \[ 7X = 8 \left( \frac{4X}{5} + 600 \right) \] ### Step 7: Distribute and Simplify Distributing the 8 gives: \[ 7X = \frac{32X}{5} + 4800 \] ### Step 8: Clear the Denominator Multiply the entire equation by 5 to eliminate the fraction: \[ 35X = 32X + 24000 \] ### Step 9: Solve for X Rearranging the equation gives: \[ 35X - 32X = 24000 \] \[ 3X = 24000 \] \[ X = \frac{24000}{3} = 8000 \] ### Conclusion The value of \( X \) is \( ₹ 8000 \). ### Final Answer (b) ₹ 8000
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