In our daily lives, we encounter at least one mathematical problem related to the unitary method. For instance, you want to buy mangoes from your favourite grocery store. You are informed by the seller that the 10 mangoes are priced at Rs. 100. However, you just need 6 mangoes and not 10. What will you do? You would use the unitary method to determine the cost of 6 mangoes based on the price the seller had mentioned. This method is something that every person should know about and should be able to calculate verbally. Even when you are preparing for various competitive exams like SSC CGL, JEE Mains, JEE Advanced, etc, the unitary method is one of the most important topics that carry a heavy weightage. Given its importance, we, through this blog, will explain everything related to the topic including the concept and important questions.
Concept of Unitary Method
Referring to as an individual or a single unit, the unitary method is used to determine the value of a single component with relation to a specific value. In other words, this is a technique where we solve a problem by finding out the value of one unit and then continue calculating the value of the other units by multiplying the former with the latter. To understand this better, let us consider the aforementioned example wherein the price of 10 mangoes is Rs. 100 and you want to purchase 6 units of mangoes.
In this case, the first thing you will calculate is the cost of 1 mango and then multiply its cost with the total number of mangoes you want. Therefore, to buy 6 mangoes, you will have to pay Rs. 60 to the seller. This is how the unitary method works!
[Cheat Code: In order to simplify the problems, we always mention the given value on the left side of the question and the value to be calculated on the right side of the equation.]
Unitary Method: Sample Questions
Let us now consider some important unitary method questions which might be essential keeping in mind the competitive exams you are preparing for.
Unitary Method Question 1. Anu earns Rs. 500 for 10 days. What will be her salary after 28 days of work?
As per the question, the 10-day salary of Anu is Rs. 500. So, let us first determine her one-day salary using the unitary method.
10-day salary of Anu = Rs. 500
1-day salary of Anu = 500/10 = Rs. 50
The total amount Anu will earn In 28 days = Rs. 50 x 28 = Rs. 1,400 [multiplying one day salary with 28 days’ salary]
Therefore, Anu will earn Rs. 1,400 after 28 days of work
Unitary Method Question 2. In an army camp, 45 soldiers can consume a stock of food for 2 months. Determine, how much time the same stock of food will last for 27 soldiers?
Let us first have a look at the given condition.
As per the question, 45 soldiers will consume the given food stock in 60 days (2 months). Therefore, the soldier-time ratio would be 45:60
According to the second condition, the same food stock is consumed by 27 soldiers in ‘y’ days. So the ratio is 27:y
As mentioned before, keep the given value on the left-hand side of the equation and the value to be determined on the right. The required equation to determine the number of days will thus be –
45 x 60 = 27 x y [To understand this, read ratio and proportion problems]y = (45 x 60) / 27
y = 100 days.
Thus, 27 soldiers will consume the food stock in 100 days.
Unitary Method Question 3. Aman finishes a piece of work in 15 days and Badri completes the same work in 10 days. If they both work together, how many days will they take to complete the same work?
Aman completes a piece of work in 15 days. Hence, his one-day work will be equal to 1/15. Similarly, the one day work of Badri will be equal to 1/10.
Total work done in a day if both Aman and Badri work together = 1/15 + 1/10
The LCM of 10 and 15 = 30
One-day work of Aman and Badri = 5/30 = 1/6
Therefore, if both Aman and Badri work together, they will complete the given piece of work in 6 days.
Unitary Method Question 4. A man travels at a speed of 140 km per hour and covers a distance of 420 km. How much time will he take to cover a distance of 280 km?
In order to solve this, we need to use the basic concepts related to time and distance questions. As per the given information, we know the speed and distance covered by the man, in order to solve the problem we need to first determine the time covered in the given condition, using the formula,
Distance = Speed x Time
On putting the values in the above formula, we get –
420 = 140 x Time
Time = 420 / 140 = 3 hours
Now, applying the unitary method, we calculate the time covered based on the distance covered.
420 km = 3 hours, then
1 km = 3 / 420 hours, so
280 km = 280 x (3 / 420) hours = 2 hours
Therefore, the man takes 2 hours to cover a distance of 280 km.
Test your Knowledge with some more questions on the unitary method.
- 4 workers are hired to complete a piece of work in 20 days. If 20 workers are employed in all, in how many days will they complete the work?
- A factory produces 62,5149 batteries in just 27 days. In how many days will the factory produce 18 batteries?
- It takes 4 hours to cover a certain distance if travelled at a speed of 60 kmph. Calculate the speed if the same distance is to be covered in 3 hours.
- If the total weight of 6 books equals 1.260 kg, then how many books should be there in all to get the weight of 3.150 kg?
- What is the cost of the fabric measuring 0.6 meters if the 0.75-meter of the same fabric costs Rs. 45?
Thus, understanding the concepts related to the unitary method is important to score well in the exam where the topic forms an integral part. If you are planning to study Management courses abroad and are in need of a good GMAT coaching in Delhi or other places, then Leverage Edu is here to make your preparations easy! Click Here to book a 30-minutes free career counselling session and get the answers to all your queries!