Question

A man had a certain amount with him. He spent 20% of that to buy an article and 5% of the remaining on the transport. Then he gifted Rs. 120. If he is left with Rs. 1400, the amount he spent on transport is:
(a) Rs. 380
(b) Rs. 61
(c) Rs. 95
(d) Rs. 80

Answer 1

Hint: First, we will suppose that he was having an amount of Rs. x with him. Then, we need to find the value of the amount spent on buying an article which is 20% of x Then, we can find the amount left after spending the amount on buying an article. After that, we can find the amount he spent which is 5% from the remaining amount for the transport. Then, using the condition of gifting and equating it with Rs. 1400, we get the actual amount he has in starting. Then we will use the amount for transportation formula as Rs. $\dfrac{4x}{100}$. Then, by substituting the value of x we get the desired transportation amount.

Complete step by step answer:
In this question, we are supposed to find the amount a man spent on transportation.
Suppose in the starting he was having an amount of Rs. x with him.
Then, we need to find the value of the amount spent on buying an article which is 20% of x.
So, we can find the amount left after spending the amount on buying an article by the expression as:
x- 20% of x
By using the above relation, we can find the amount of the money left after buying an article as:
$\begin{align}
  & x-\dfrac{20}{100}\times x=\dfrac{100x-20x}{100} \\
 & \Rightarrow \dfrac{80x}{100} \\
\end{align}$
So, he is left with Rs. $\dfrac{80x}{100}$ after buying an article.
Then, he spent 5% from the remaining amount for the transport as:
So, we will calculate the 5% of the remaining amount which is Rs. $\dfrac{80x}{100}$ as:
5% of $\dfrac{80x}{100}$
$\Rightarrow \dfrac{5}{100}\times \dfrac{80x}{100}=\dfrac{4x}{100}$
Now, to get the amount he has left with after spending on transportation is given by:
$\dfrac{80x}{100}-\dfrac{4x}{100}=\dfrac{76x}{100}$
Then, he gifted Rs. 120 and still left with Rs. 1400.
So, the expression referring to the above condition is as:
$\dfrac{76x}{100}-120=1400$
Now, solving the above stated expression to get the value of x as:
$\begin{align}
  & \dfrac{76x}{100}=1520 \\
 & \Rightarrow x=\dfrac{1520\times 100}{76} \\
 & \Rightarrow x=2000 \\
\end{align}$
So, the original amount a man has in the starting is Rs. 2000.
Now , to calculate the expenditure on the transportation we will use the expression of the cost on transportation calculated above as Rs. $\dfrac{4x}{100}$.
So, substitute the value of x as 2000 and calculate the value of the amount spent on transportation as:
$\dfrac{4\times 2000}{100}=80$
So, Rs. 80 is spent on transportation.
Hence, option (d) is correct.

Note: The most common mistakes we occur in this type of the questions is that when we get the first reduction in the original value that is in this question amount spent on buying an article, we get$\dfrac{80x}{100}$ but after that we forgot to see the word remaining and proceed with the amount spent on the transportation as 5% of x which gives us $\dfrac{5x}{100}$. Instead of taking 5% of the remaining amount that is $\dfrac{80x}{100}$ if we got with $\dfrac{5x}{100}$then there is a mismatch of answers. We will get answer as:
$\dfrac{5\times 2000}{100}=100$
We will get an answer as Rs. 100 which is an incorrect answer.