Question

If the price of sugar decreases by Rs 5 ,one can buy 1 kg more sugar at Rs 150, what is the price of the sugar?

Answer 1

Hint: We get the price of same x kg of sugar values Rs 150, but decrease in Rs 5 increase $1kg$ of sugar in Rs 150 means he can buy for $x + 1\;kg$ compare and find the Rs value Per kg.

Complete step-by-step answer:
Let’s begin with the amount of sugar with Rs 150 can be bought is $x kg$ or we can see, the Amount of 1 kg sugar increases if the price per kg decreases.
Let’s assume that the price of 1 kg of sugar is M and no. of kg can be bought initially is 150/M. If the value of M decreases by 5, then the 150/M-Skg he can buy now.
As we know, the no. of kg initially he can buy and now he can buy is having a difference of 1 kg. so we get expression as
$So\dfrac{{150M - \left( {150M - 750} \right)}}{{M\left( {M - 5} \right)}} = 1$
$ \Rightarrow \dfrac{{750}}{{M\left( {M - 5} \right)}} = 1$
By cross multiplying we get,
$ \Rightarrow M\left( {M - 5} \right) = 750$
$ \Rightarrow M_{}^2 - 5M - 750 = 0$
$M_{}^2 + 25M - 30M - 750 - 0$
$ \Rightarrow M\left( {M + 25} \right) - 30\left( {M + 25} \right) = 0$
$ \Rightarrow \left( {M + 25} \right)\left( {M - 30} \right) = 0$
$M = - 25\;and\;M = 30$
The price of an object can never be negative so the answer for per kg price of sugar is Rs 30.

Note: There can be mistakes while subtracting two values which results 1, but for the same numerator, greater the value of denominator will result in a smaller value.