Inverse Case – Value From Percentage

You must have definitely prepared percentage topic for the exams. But the topic is so diversified that it becomes hard for a student to fully comprehend it. We all have been taught to find the percentage of the given values. But what would happen if it is reversed? How to find value from percentage?

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Value from Percentage                                                                                                                           

There is never a set pattern in a competitive exam. And there have been questions from the past exams, where a candidate was asked to find the value from the percentage. So it becomes very important that you prepare such topics. Generally, these below types of questions are asked in the exams.

Solved Example

Q. Anil gets a tuition fee of Rs. 200 per week. Now, he asks for a raise of 15 %. What will be his revised fees per week?

A. Rs. 210
B. Rs. 230
C. Rs. 200
D. Rs. 245

This question can be solved using two methods.

Method 1

In method 1, you can use directly the multiplying factor for the 15 % raise given in the question. Here, 1.15 will be the multiplying factor. So, the increase in the fee that Anil asks will be (100 % + 15 %) of 200
= 115 % of 200
= 1.15 x 200
= 230.
So, after increasing Anil’s salary will be Rs. 230.

Method 2

Method 2 can only be used if the questions asked are less complex. In this method, you can do the calculations quickly and find the answer. Here, the raise asked is 15 %. So we can divide it into two parts 10 % and 5 %. 10 % of 200 will be 20 and 5 % will be 10. So, by adding both the values we will get 30. Add this to 200. So, after the rise, his salary will be Rs. 230.

So, the correct answer is B.

In the above example, we saw the multiplying factor. To find the multiplying factor, there is a direct formula used which is as under:
For an increase of a % in the value of b, the multiplying factor is ( 1+ p/100) and the final value will be given by,
Final value = (1 + p/100) x q

For a decrease of a % in the value of b, the multiplying factor is (1 – a/100)
And again the final value will be given by,
fv = (1 – p/100) x q
where, fv = final value.

Examples of Finding the Value Using Percentage

Q. The daily salary of Rahul is Rs. 200 and the tax deducted at source is 15 %, then find the net salary of Rahul per day.

A. Rs. 160
B. Rs. 165
C. Rs. 170
D. Rs. 180

In this question, we need to find the daily salary of Rahul i.e value from percentage given in the question. Usually, daily net salary or any net salary can be found after deducting the taxes and expenses from the gross salary.

So, net salary = gross salary – deductions

= 100 % of salary – 15 % of his salary
= 85 % of 200 = 0.85 x 200 = Rs. 170.

Here the multiplying factor is 0.85. This multiplying factor can also be described as a fraction, for example, 0.85 = 85/100 = 17/20.

Finding the initial value, when the final value and the percentage is given to us.

Q. The new fares of the train from Pune to Hyderabad was increased by 9 % and Suresh ended up paying Rs. 5995. Find the initial fare before the hike.

A. Rs. 5500
B. Rs. 5600
C. Rs. 5700
D. Rs. 5800

Here, in this type of questions you just need to find the initial fare before the prices were increased. You can also solve this question by using a multiplying factor.

Here, the fares are increased by 9 % so the multiplying factor will be 1.09. Now let the initial fare be Rs. x. And the final value is y = 5995.
Therefore, y = 1.09x, x = y/1.09 = 5995/1.09 = 5500. So, the correct answer is Rs. 5500 which is option A.

Practice Questions

Q. In order to clear the exam candidates were asked to take an aptitude test. Every candidate must score 60 % marks. Hiral took the test and missed the cut off by 8 marks. She scored 40 marks. What were the maximum marks in the test?

A. 120
B. 160
C. 80
D. 72

Ans: The correct answer is C.

Q. Instead of finding 50 % of the number, Mahesh finds 15 % and gets a value which is 140 less. Find this number.

A. 280
B. 400
C. 80.5
D. 200

Ans: The correct answer is B.

Q. To pass the exam every candidate need to score 35 % of the total marks in the exam. A student got 35 marks and failed by 35 marks. What were the maximum marks for the test?

A. 200
B. 130
C. 100
D. 70

Ans: The correct answer is A.

Q. When 60 % of a number is added to 60 the original number is obtained. Find the original number here.

A. 150
B. 160
C. 96
D. No such number is possible

Ans: The correct answer is A.

Q. The population in the village is 5500. If the number of females increases by 20 % and the number of males increases by 11 %, the population becomes 6330. Find the number of females in the village.

A. 3000
B. 2000
C. 2500
D. 3500

Ans: The correct answer is C.

Q. Ajay bought goods worth Rs. 6000. He gets a rebate of 10 % on it. After getting the rebate, he pays sales tax of 20 %. What is the amount that Ajay has to pay for goods?

A. Rs. 6480
B. Rs. 6280
C. Rs. 6330
D. Rs. 6440

Ans: The correct answer is A.