Question

Find the value of x if it is given that 30% of 140 = x% of 840.
a. 5
b. 15
c. 24
d. 60

Answer 1

Hint:In order to find the solution of this question, we should know that percentage refers to the parts per 100, or we can say that x percentage of some number is the $ {{x}^{th}} $ part of that number per hundred. By using this concept, we will find the solution to this question.

Complete step-by-step answer:
In this question, we have been asked to find out the value of x, when it is given that 30% of 140 = x% of 840. To solve this question, we should know that percentage refers to the parts per 100, or we can say that x percentage of y is as same as the $ {{x}^{th}} $ part of y per hundred or we can say that, $ \dfrac{x}{100}\times y $ .
So, we can say that, 30% of 140 can be written as, $ \dfrac{30}{100}\times 140 $ and x of 840 can be written as, $ \dfrac{x}{100}\times 840 $ . Therefore, we can say that, 30% of 140 = x% of 840 can be written as,
 $ \dfrac{30}{100}\times 140=\dfrac{x}{100}\times 840 $
Now, we will keep the variable on one side and take all the numbers to the other side. So, we will get,
 $ x=\dfrac{30\times 140\times 100}{100\times 840} $
Now, we know that the common terms in the numerator and the denominator gets cancelled out. So, we get,
 $ x=\dfrac{30\times 14}{84} $
And we know that it can be further expressed as,
x = 5
Hence, we can say that the value of x is obtained as 5. Therefore, we get option (a) as the correct answer.

Note: While solving this question, the possible mistake which we can make is the calculation mistake. Also, we can solve this question by putting the values of x from the option one by one and then checking which value of x satisfies the given condition, but by using this method, the solution will become lengthier and it will be time consuming. So, it is better to use the conventional method to solve this question. We need to just apply the basic definition of percentage and solve the two given equations to get the desired result.