A trader purchases a watch and a wall clock for Rs. $390$ . He sells them making a profit of $10 %$ on the watch and $15 %$ on the wall clock. He earns a profit of Rs. $51.50$ . The difference between the original prices of the wall clock and the watch is equal to

Rs.

110

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Rs.

100

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Rs.

80

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Rs.

120

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Solution

The correct option is A Rs. $110$
Let the cost of the watch $=$ Rs. $x$ .
Then, cost of the clock $=$ Rs. $(390 - x)$
Given, $10 %$ of $x + 15 %$ of $(390 - x) = 51.50$
$\Rightarrow \frac{x}{10} + \frac{15 \times (390 - x)}{100} = 51.50$
$\Rightarrow 10 x + 5850 - 15 x = 5150$
$\Rightarrow 5 x = 700$
$\Rightarrow x = 140$
$∴$ Cost of clock $=$ Rs. $(390 - 140) =$ Rs. $250$
$∴$ Required difference $=$ Rs. $250 -$ Rs. $140 =$ Rs. $110$ .

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A trader purchases a watch and a wall clock for Rs. 390. He sells them making a profit of 10% on the watch and 15% on the wall clock. He earns a profit of Rs. 51.50. The difference between the original prices of the wall clock and the watch is equal to

A trader purchases a watch and a wall clock for Rs. $390$ . He sells them making a profit of $10 %$ on the watch and $15 %$ on the wall clock. He earns a profit of Rs. $51.50$ . The difference between the original prices of the wall clock and the watch is equal to