You won’t find many questions from inequality in a competitive exam. But still, you need to practice all type of questions to cover the whole syllabus. One such type of inequality question that can be asked in the competitive exam is word problems. We will try and cover some of the basics related to word problems.
Questions from word problems will be similar to the ones asked in inequality. The only difference between the two is that in word problem you are given the question in the form of the words.
You will be given multiple sentences in the question and you need to try and form an equation, from this question. The data will be given to you in the form of the words and you need to find the inequality equation that will best represent the given data. Here are the solved examples that will help you understand the topic better.
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1. Ajay and Sanjay were the two brothers and they decided to put up a fence around their rectangular farm. They have 60 feet of fence and wants their farm to be 20 feet wide. What will be the inequality equation that will best represent the possible length of their farmyard?
A. 8 feet B. 10 feet C. 12 feet D. 15 feet
Ans: In this question, we are required to find out the possible length of the farm. We need to find the inequality formula to find the length. The formula for the perimeter of a rectangle is 2l + 2b, where l is for length and b is for breadth. As given in the question the total perimeter required should be less than or equal to 60, because that is the amount of fencing Ajay and Sanjay has for their farm.
So, the inequality formula here will be, 2l + 2b ≤ 60. But the breadth (width) is given to us in this question. So, we will replace b by 20 feet. Thus, the above formula will be written as,
2l + 40 ≤ 60. Now, we need to solve this equation to find the possible length of the farm. So, the given will be,
2l + 40 ≤ 60
2l + 40 – 40 ≤ 60 – 40
2l ≤ 20
2l/2 ≤ 20/2
l ≤ 10
Thus, the required possible length for the farm is 10 feet. So, the correct answer is B.
Word Problems on Profit and Loss
Q. Bhavesh sells his books in the flea market. He makes a flat profit of Rs. 2 per book, but he is required to pay a monthly rent of Rs. 4 per month to the owner of the shop. How many books should Bhavesh sell so that could at least make Rs. 120 per month?
A. Rs. 62 B. Rs. 64 C. Rs. 65 D. Rs. 66
Ans: Let’s assume that x is the number of books that Bhavesh sells per day. To find out how much does Bhavesh earns in the entire month we can multiply the number of books Bhavesh sold by the profit he earns on one book and then subtract the Rs. 4 rent per month to find how much he makes in an entire month.
We are given that the profit should be Rs. 120 per month. And we are required that the number should be greater than or less than 120, so the equation will be,
2x – 4 ≥ profit per month.
2x – 4 ≥ 120
Now, add 4 on both the sides of the equation. Thus the equation will become,
2x – 4 + 4 ≥ 120 + 4
2x ≥ 124
2x/2 ≥ 124/2
x ≥ 62
So, Bhavesh will make Rs. 62 per month by selling the books. Thus, the correct answer is A.
A. Shaym wants to buy elephants, and for every elephant, he needs to buy 2 acres of land. If there are 16 acres of land already available to him how many elephants can he buy? Describe it in inequality equation.
A. b < 18 B. b > 18 C. b ≤ 16 D. 2b ≤ 16
The correct answer is D.
2. A student is thinking of taking classes to improve his maths. The classes charge Rs. 40 for an hour. But the student can only afford to pay Rs. 200 for the classes. Describe the classes that the student can attend in the inequality equation.
A. 40x ≤ 200 B. 4x < 200 C. 40x = 200 D. 40x > 200
The correct answer is A.
3. There are 6 oranges required to make a fruit dish. If there are 24 oranges available, write the equation to represent the number of fruit dishes that can be made.
A. 6a > 24 B. 6a < 24 C. 6a ≤ 24 D. 6a = 24
The correct answer is C.