# How to Solve the Questions of Unitary System With Three Variables

**How to Solve the Questions of Unitary System With Three Variables**: The questions on **Unitary System With Three Variables **are generally part of every competitive exam, these arithmetic questions of **Unitary System** are studied in 7 and 8-grade maths book of CBSE and you can see these questions in 9 and 10-grade maths book of some of the state board. **Unitary System** is the way of solving the unknown quantity, according to the hints are given in the question,in the solutions of such questions.

In solving the questions based on **Unitary System** we have to determine the value of unit quantity by dividing the value of the given quantity from the corresponding number of quantities and then we can calculate the value of the asked quantity by multiplying the value of unit quantity with a number of quantities whose value is asked in the question.

Here few selected questions are solved by a step-by-step method. The solutions are given when two or three variables exist in the questions. You can study here NCERT Solutions of science and maths, articles on science and maths, sample papers, solutions of previous years’ question papers, competitive entrance exams, and online jobs.

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**How to Solve the Questions of Unitary System With Three Variables**

**UNITARY SYSTEM- **In such questions, two or three variables are given in such a way that both of or three of them depend on each other or both or three of them varies against each other or one another, the way of calculating unit (1) value of one quantity in terms of changes in the value of other quantity is known as a unitary system. Here at Future Study Point, now you can clear your concept through the solution of questions involving two-variable and three variables. Such questions you have studied in class 5 or 6 . The questions on the unitary system are the part of the maths syllabus in 5 to 8 th class compulsorily. These questions on the unitary system are of two types, (a) Two variable (b) Three variable

**Questions and answers on Unitary System when two and three variables are given**

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**(a) Solutions of Questions On Unitary System With Two Variables **

** Q1. 5 kg potaoes cost Rs 50 then find the cost of 3 kg potatoes.**

Ans. In the solution of these questions place the value of the variable in the extreme right and left corners of the statement after and before of the sign of equal (=).

As in this question, we have to calculate the cost of potatoes, let’s place the cost on the right side of the statement, and at the start of the sentence write the quantity whose cost is given. Now in the second line of statement calculate the cost of one unit quantity by dividing the given cost( Rs 50) from the given quantity (5 kg). Finally in the third line of statement get the cost of given quantity(5 kg) by multiplying the figure(i.e Rs 10) you got in the second line.

Therefore cost of 3 kg potatoes is Rs = Rs 30

**Q2. 5 men can plant 500 plantlets of paddy in a day, if they work 4 hours in a day . How many persons are required to plant the same number of plantlets in a day if they work 3 hours a day?**

Ans. Here number of days and number of plants are not variable because in the questions number of days and plants are fixed.

The working hours and number of men are variables, so the way of calculation is the same as in previous question

First of all, think what is the variable you have to find out in the questions, write that variable towards the extreme right after the sign of equal

The rest of one variable must be placed in the left side of the statement, as in the given question we have to find out the number of men so , following the above procedure in the question.

500 plantlets of paddy planted working 4 hours a day by= 5 men

500 plantlet of paddy planted working 1 hours a day by = 5 ×4 = 20 men

∴ 500 plantlet of paddy planted working 3 hours a day by = 20/3 ≈7

Therefore almost 7 men are required to plant 500 plantlets in a day if they work 3 hours a day.

**HINT-** In the unitary system if a decrease or increase in one quantity affecting the other quantity to increase then there should be multiplication and if decrease or increase in one quantity affecting the other quantity to decrease then there should be a division.

**(b) Solutions of Questions On Unitary System With Three Variables **

In the case when three variables are given-In the above question (a) 2 if the number of plantlets also changes then there will become three variables as shown below.

**Q3. 5 men can plant 500 plantlets of paddy in a day if they work 4 hours in a day. How many persons are required to plant 600 of plantlets in a day if they work 3 hours a day?**

Answer- We are asked here how many numbers of persons are required to plant 600 of plantlets in a day if they work 3 hours a day

We have to determine the number of persons so write the number of persons in the extreme right of the statement.

While writing the next line of answer determine the number of persons required to plant 1 plantlet keeping the value of other variable(hours) same in the left part of the statement.

Thereafter in third line determine the number of persons required to plant 600 plantlets keeping the number of hours same. Follow the same procedure for second variable (number of hours) ,see the solution.

Ans. 500 plantlets can be planted working 4 hours a day by = 5 men

1 plantlet can be planted working 4 hours a day by = 5/500 men

600 plantlet can be planted working 4 hours a day by = (5/500) × 600 men

600 plantlet can be planted working 1 hour a day by = (5/500) × 600×4 men

600 plantlet can be planted working 3 hour a day by

Therefore 8 men are required to plant 600 plantlets in a day if they work 3 hours a day

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