Question

A person purchases one kg of tomatoes from each of the $4$ places at the rate of $1$ kg, $2$kg, $3$kg, $4$kg per rupee respectively. On the average he has purchased $x$ kg of tomatoes per rupee, then the value of $x$ is
$(A)2$
$(B)2.5$
$(C)1.92$
$(D)$ None of these

Answer 1

Hint: Here a person purchases one kg of tomatoes from $4$places so total quantity of tomatoes is $4$kg. Then we need to find the total money, here the rate of $1$ kg, $2$kg, $3$kg, $4$kg per rupee is given. So sum up the rate of kg we get the total money. From that we can find the average by dividing.

Complete step-by-step answer:
A person purchases one kg of tomatoes from each of the $4$places. We have to find the total quantity that a person purchased. For that we have to multiply,
$\Rightarrow $ Total quantity of tomatoes purchased$=4\times 1$
$\Rightarrow $ Total quantity of tomatoes purchased$=4$ kg
Then we need to find the total money for which we have the rate of $1$ kg, $2$kg, $3$kg, $4$kg per rupee.
The rate of $1$kg per rupee means that $\dfrac{1}{1}$
The rate of $2$kg per rupee means that $\dfrac{1}{2}$
The rate of $3$kg per rupee means that $\dfrac{1}{3}$
The rate of $4$kg per rupee means that $\dfrac{1}{4}$
Adding all the values we get the total money,
$\Rightarrow $ Total money$=\dfrac{1}{1}+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}$
 Taking LCM we get,
$\Rightarrow $ Total money$=\dfrac{12+6+4+3}{2}$
$\Rightarrow $ Total money$=\dfrac{25}{12}$
Then we need to find the value of $x$ that means we have to find the average,
$\Rightarrow $ Average$=\dfrac{4kg}{TotalMoney}$
$\Rightarrow $ Average$=\dfrac{4}{\dfrac{25}{12}}$
Take the $12$ to numerator we get,
$\Rightarrow $ Average$=\dfrac{12\times 4}{25}$
On doing further we get,
$\Rightarrow $ Average$=\dfrac{48}{25}$
$\Rightarrow $ Average$=1.92$
On the average he has purchased $x$ kg of tomatoes per rupee, then the value of $x$ is $1.92$ .

Note: We are given that rate per rupee so we can also use harmonic means to get the value of $x$. The harmonic mean is a type of numerical average. It is calculated by dividing the number of observations by the reciprocal of each number in the series.