A clock was sold for Rs 144 If the percentage of...

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A clock was sold for Rs. 144. If the percentage of profit was numerically equal to the cost price, the cost of the clock was -

A. Rs. 72

B. Rs. 80

C. Rs. 90

D. Rs. 100

Answer: Option B

Solution(By Examveda Team)

Let,
C.P. = Rs. x,
Profit% = x% and
S.P. = Rs. 144
$$\eqalign{ & \therefore x = \left[ {\frac{{100}}{{\left( {100 + x} \right)}} \times 144} \right] \cr & \Rightarrow {x^2} + 100x = 14400 \cr & \Rightarrow {x^2} + 100x - 14400 = 0 \cr & \Rightarrow {x^2} + 180x - 80x - 14400 = 0 \cr & \Rightarrow \left( {x + 180} \right)\left( {x - 80} \right) = 0 \cr & \Rightarrow x = 80 \cr} $$

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Comments ( 2 )

Mohammad Javed :

3 years ago

This type of question should be solved by option
From option (B)
Sp=80+80*80/100
=144 which is satisfied .
Thus correct ans will be 144.
OR//
Another highly useful method
Break the given sp in such a way that their difference is 10 and multyply by 10 both the factors. If profit is gained then smaller factor is our ans .If loss is gained then bigger factors is our ans.
Viz 144 =8*18 having difference 10
Not 144 factorize as 12*12 or 16*9 because thse factors not differed by 10.
Here profit is gained so our ans is 8*10 ie 80
Thus correct ans is 80
Srishti Dixit :

4 years ago

In this well we can also factor as 100 and 144 then??