Question

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. Rs.110
B. Rs.100
C. Rs.80
D. Rs120

Answer 1

Hint: Assume cost price of watch as variable and calculate the cost price of clock using the total amount given. Calculate profit value of each using the formula of profit from percentage given. Add the both profit values and equate to the given price. Calculate the value of the variable from the equation formed. Subtract the cost price of the wall clock and watch.
* We calculate the percentage of a number x as \[\dfrac{m}{{100}} \times x\].

Complete answer:
Let us assume the cost price of watch as Rs.x
We know that trader purchased watch and clock for Rs.390
So, cost price of the clock will be Rs.\[(390 - x)\]
Now we are given that he earned profit of \[10\% \] on the watch and \[15\% \] on the wall clock
Then price of profit earned with each item will be given by multiplying the percentage of profit with the cost price of the item
\[ \Rightarrow \]Profit on watch\[ = 10\% (x)\]
Use method of percentage
\[ \Rightarrow \]Profit on watch\[ = \dfrac{{10x}}{{100}}\] … (1)
Similarly,
\[ \Rightarrow \]Profit on wall clock\[ = 15\% (390 - x)\]
Use method of percentage
\[ \Rightarrow \]Profit on wall clock\[ = \dfrac{{15(390 - x)}}{{100}}\] … (2)
Since we are given that he earns a profit of Rs.51.50
We can add the profits from equations (1) and (2) and equate to Rs.51.50
\[ \Rightarrow \dfrac{{10x}}{{100}} + \dfrac{{15(390 - x)}}{{100}} = 51.50\]
Convert the decimal number in right hand side of the equation
\[ \Rightarrow \dfrac{{10x}}{{100}} + \dfrac{{15(390 - x)}}{{100}} = \dfrac{{5150}}{{100}}\]
Cancel same factor i.e. 100 from both sides denominators
\[ \Rightarrow 10x + 15(390 - x) = 5150\]
\[ \Rightarrow 10x + 5850 - 15x = 5150\]
Shift constant values to right hand side of the equation
\[ \Rightarrow 10x - 15x = 5150 - 5850\]
\[ \Rightarrow - 5x = - 700\]
Cancel same factors from both sides of the equation i.e. -5
\[ \Rightarrow x = 140\]
So, cost price of watch is Rs.140
We can write the cost price of a clock is \[390 - 140 = 250\] i.e. Rs.250
We have to calculate the difference in price of items
Difference between price of watch and wall clock is \[250 - 140 = 110\]
\[\therefore \]The difference in price is Rs.110

\[\therefore \]Option D is correct.

Note: Many students make the mistake of calculating the value of profit wrong as they only write 10% and 15% but don’t multiply it with respective cost prices. Keep in mind profit is always with reference to some price, so we will have to multiply percentage with the respective price.