Question

One kg of tea and one kg of sugar together cost 95. If the price of tea falls by 10% and that of sugar rises by 20%, then the price of one kg of each combined comes to Rs.90. Find the original price of tea.

Answer 1

Hint: We will assume the price of tea to be any variable say x and price of sugar as y. Then we will make a linear equation by using the statement given in question. We will use the fall in tea price i.e. $x-10\%x$ and that rise in price of sugar as $y+20\%y$ . So, there will be two linear equations with us. Then we will use the substitution method i.e. putting the value of one variable in another equation and by doing this we will find the value of both the variables. Thus, we will get our required answer.

Complete step by step answer:
Here, we will assume the price of tea as x and that of sugar as y. It is given that one kg of tea and one kg of sugar together cost Rs.95. So, we can write in mathematical form as
$x+y=95$ ……………………………………..(1)
Now, it is given that there is a 10% fall in the price of tea which means a discount on tea. So, we have to deduct 10% of x from x and we can write it as
$x-10\%x$
On solving, we get
$x-\dfrac{10}{100}x$
On taking LCM, and further simplifying we get
$\dfrac{10x-x}{10}=\dfrac{9x}{10}=0.9x$ ………………………….(2)
Similarly, it is given that there is a 20% rise in sugar price. It means that we have to add 20% of y to y. So, in mathematical form, we can write it as
$y+20\%y=y+\dfrac{20}{100}y$
On further simplification, we get
$=\dfrac{10y+2y}{10}=1.2y$ ………………………………….(3)
After this fall in tea price and rise in sugar, the total price becomes Rs. 90. So, we will add equation (2) and (3) and we will get as
$0.9x+1.2y=90$ ………………………………….(4)
Now, from equation (1) we will make variable y as subject and we get as $y=95-x$ and substituting this value in equation (4), we get
$0.9x+1.2\left( 95-x \right)=90$
On solving the brackets, we get
$0.9x+114-1.2x=90$
On further simplifying, we get
$-0.3x=90-114=-24$
$x=\dfrac{-24}{-0.3}=80$ …………………………….(5)
Substituting this value of equation (5) in equation (1), we get
$80+y=95\Rightarrow y=95-80=15$
Thus, original price of tea is x i.e. Rs.80.

Note: Be careful in using discount formula i.e. $x-10\%x$ . Most mistakes happen when students write the formula as $x-10\%$ . This will lead to incorrect answers. Always remember discount is on price of object. Here, it is tea so the discount should be on the price of tea i.e. $10\%x$ and then subtracting this from the original price of tea which will give us $x-10\%x$ . So, do not make this type of mistake. Also, do not assume the price of tea and sugar to be Rs. 100 and then try to solve. Here, you will not get the original price of tea and sugar and it will become very confusing. So, use a linear equation in this type of problem.