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