Question

A dishonest dealer professes to sell his goods at cost price. But he uses a false weight and thus gains $6\dfrac{{18}}{{47}}$% for a kg, he uses a weight of
$
  (a){\text{ 940gms}} \\
  (b){\text{ 947gms}} \\
  (c){\text{ 953gms}} \\
  (d){\text{ 960gms}} \\
$

Answer 1

Hint: In this question let the correct weight be 1000gm and the incorrect weight be x gm, equate the percentage gain given in question with the calculated percentage of difference in weights obtained. This will help to get the answer.

Complete step-by-step answer:
Let the incorrect weight of the goods = x gm.
Correct weight = 1000 gm.
So the difference of weight = correct weight – incorrect weight
                                                  = (1000 – x) gm.
Now the percentage gain (P.G) is the ratio of difference in weight to the correct weight multiplied by 100.
 $ \Rightarrow P.G = \dfrac{{1000 - x}}{{1000}} \times 100$............................. (1)

Now it is given that P.G = $6\dfrac{{18}}{{47}}$%
Now convert this fraction into improper fraction we have,
$ \Rightarrow 6\dfrac{{18}}{{47}} = \dfrac{{6 \times 47 + 18}}{{47}} = \dfrac{{300}}{{47}}$

Now substitute the value in equation (1) we have,
$ \Rightarrow \dfrac{{300}}{{47}} = \dfrac{{1000 - x}}{{1000}} \times 100$

Now simplify the equation we have,
$ \Rightarrow \dfrac{{300}}{{47}} = \dfrac{{1000 - x}}{{10}}$
$ \Rightarrow 3000 = 47000 - 47x$
$ \Rightarrow 47x = 47000 - 3000 = 44000$

Now divide by 47 we have,
$ \Rightarrow x = \dfrac{{44000}}{{47}} = 936.17 \simeq 940$ gm.

Hence option (A) is correct.

Note: The trick point here was to take the correct weight as 1000 gm, the main reason behind this was to synchronize the relations with respect to 1000gm, because the percentage gain of the dishonest dealer is given for 1 kg and 1kg is equal to 1000gm.