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REET Level 1+2 . Maths

Unitary Method - REET Maths Notes

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The Unitary Method is the foundation for real-life questions in REET Maths - from the market to the mid-day meal scheme. This page clarifies the difference between direct and inverse proportion, with worked examples and REET 2024's questions.

  • 2 questions in REET 2024
  • Class 5-7 level
  • 6 min read
Verified 17 September 2026 · Source: NCERT Class 6-8 Maths textbooks (official)

How REET asks this topic

Both REET 2024 questions were based on everyday contexts - one required finding the unit price of pens and counting how many could be bought in a given amount, the other required finding the total quantity of grain needed for 60 children over 30 days under the mid-day meal scheme. In other words, this isn't tested through a plain formula, but through finding the unit value in a real situation and applying it correctly.

What is the unitary method

In the unitary method, you first find the value of one unit, and then use that unit value to work out the value of the required quantity. This method is used in two kinds of situations - direct proportion and inverse proportion.

In direct proportion, when one quantity increases, the other increases in the same ratio - for example, as the number of items increases, the total cost also increases. In inverse proportion, when one quantity increases, the other decreases in the same ratio - for example, as the number of workers increases, the time taken to complete the work decreases (when the total work stays the same).

Worked example 1: the price of pens

REET 2024 asked: if four dozen pens cost Rs 120, how many pens can you buy for Rs 35? Four dozen = 4x12 = 48 pens. Unit price = 120/48 = Rs 2.50 per pen. So for Rs 35, number of pens = 35/2.50 = 14 pens.

Worked example 2: the mid-day meal scheme

One of REET 2024's questions was based on the mid-day meal scheme. Per government norms, each child at the upper primary level (Classes 6-8) is given 150 grams of grain (rice/wheat) per day, while at the primary level (Classes 1-5) this amount is 100 grams per day. Suppose grain needs to be ordered for 30 days for 60 children in a school's upper primary section - total grain = 150 x 60 x 30 = 2,70,000 grams = 270 kg. Note that the daily amount per child must be multiplied by both the number of children and the number of days - a single step alone won't give the correct answer.

Direct vs inverse proportion - how to tell them apart

Example of direct proportion
The number of items and their total cost - both increase and decrease together.
Example of inverse proportion
The number of workers doing a fixed job and the time taken - as one increases, the other decreases.
How to check
First ask yourself - 'will the second quantity increase or decrease along with the first?' Choose the right kind of proportion based on the answer.

Worked example: inverse proportion

4 women complete a piece of work in 6 days; in how many days will 3 women complete the same work? This is inverse proportion because reducing the number of workers will increase the time taken. Total work = 4x6 = 24 woman-days (this stays constant). So for 3 women, days = 24/3 = 8 days.

The same logic applies to pipe-and-tank questions - the more taps you open together, the faster the tank fills, assuming all the taps flow at the same rate. This understanding of the unitary method is the foundation of the later 'Time and Work' topic.

Worked example: direct proportion (fuel consumption)

If a vehicle needs 12 litres of petrol to travel 150 kilometres, how much petrol is needed to travel 250 kilometres? This is direct proportion because petrol consumption increases as distance increases. Unit rate = 12/150 = 0.08 litres per km. So petrol needed for 250 km = 250x0.08 = 20 litres.

How to teach this to children

Classroom activity

In Classes 5-6, run a market-shop role-play activity - like buying a notebook and pencil - where students first find the price of one item, then work out how many items can be bought for a given amount.

Teaching aids

Solve a real school situation like the mid-day meal scheme as a worked example in class - this is a familiar context for children and makes the concept memorable.

Common misconception

Children often multiply or divide straight away in every situation, without checking whether the relationship is direct or inverse - for example, mistakenly multiplying instead of dividing (or vice versa) in worker-day questions.

Assessment idea

Create real word problems based on local market rates (like the price of vegetables or a notebook) and have students solve them and cross-check each other's answers.

Cross-curricular link

Use a real ration register from the school's mid-day meal scheme and have children work out the quantity of grain themselves - this activity connects school administration with maths.

Trick to remember / exam tip

Before solving any question, pause for a moment and ask - 'when one quantity increases, will the other increase or decrease?' If both increase or decrease together, it's direct proportion (solve by multiplying), and if one increases while the other decreases, it's inverse proportion (solve by keeping the product constant) - asking yourself this one question prevents most mistakes in unitary method questions.

Questions asked in REET 2024 (with solutions)

Question 101

If the cost of four dozen pens is ₹ 120, then how many pens can be purchased for ₹ 35 ?

  1. A10
  2. B12
  3. C24
  4. D14

Explanation

चार दर्जन = 4 × 12 = 48 पेन, जिनका मूल्य ₹120 है। अतः 1 पेन का मूल्य = 120/48 = ₹2.50। ₹35 में पेन = 35/2.5 = 14 पेन।

Question 119

In mid-day meal, at the rate of 150 gm wheat and 100 gm rice per child per day, the total quantity of wheat and rice for 30 days for 60 children is

  1. A450 किग्रा
  2. B180 किग्रा
  3. C270 किग्रा
  4. D400 किग्रा

Explanation

प्रति बालक प्रति दिन कुल अनाज = 150 + 100 = 250 ग्राम। 60 बच्चों के लिए 30 दिन में = 250 × 60 × 30 = 4,50,000 ग्राम = 450 किग्रा। विकल्प (C) 270 किग्रा केवल गेहूँ की मात्रा है।

Practice Questions

Question 1

If the price of 5 notebooks is ₹75, what will be the price of 8 notebooks?

  1. A₹100
  2. B₹110
  3. C₹120
  4. D₹130

Explanation

Unit price = 75/5 = Rs 15; cost of 8 notebooks = 8x15 = Rs 120.

Question 2

If 12 workers complete a task in 8 days, in how many days will 6 workers complete the same task?

  1. A4
  2. B12
  3. C16
  4. D24

Explanation

Total work = 12x8=96 worker-days (inverse proportion). Days for 6 workers = 96/6=16.

Question 3

If 15 books weigh 6 kg, what will 25 books weigh?

  1. A8 किग्रा
  2. B9 किग्रा
  3. C10 किग्रा
  4. D12 किग्रा

Explanation

Unit weight = 6/15=0.4 kg; weight of 25 books = 25x0.4=10 kg.

Question 4

If a tap fills 240 litres of water in 8 hours, how much water will it fill in 5 hours at the same rate?

  1. A120 लीटर
  2. B135 लीटर
  3. C150 लीटर
  4. D160 लीटर

Explanation

Rate per hour = 240/8=30 litres; in 5 hours = 5x30=150 litres.

Question 5

Which of the following examples represents an inverse proportion?

  1. Aवस्तुओं की संख्या और कुल मूल्य
  2. Bकिसी कार्य को पूरा करने में लगे मज़दूरों की संख्या और लगने वाला समय
  3. Cदूरी तय करने पर लगने वाला पेट्रोल
  4. Dकपड़े की लंबाई और उसका मूल्य

Explanation

For a fixed amount of work, more workers means less time - this is inverse proportion. The other three examples are direct proportion.

Question 6

The price of 4 dozen bananas is ₹192. How many bananas can be bought for ₹40?

  1. A8
  2. B10
  3. C12
  4. D15

Explanation

4 dozen=48 bananas, unit price=192/48=Rs 4. Bananas for Rs 40 = 40/4=10.

Question 7

If 20 metres of cloth costs ₹1500, how many metres will be available for ₹2250?

  1. A25
  2. B28
  3. C30
  4. D35

Explanation

Unit price = 1500/20 = Rs 75/metre. Metres for Rs 2250 = 2250/75=30.

Question 8

In the mid-day meal scheme, each child is given 100 g of rice per day. How much total rice is needed for 45 children over 10 days?

  1. A40 किग्रा
  2. B45 किग्रा
  3. C50 किग्रा
  4. D90 किग्रा

Explanation

Total rice = 100 grams x 45 x 10 = 45,000 grams = 45 kg.

Question 9

The first step in the unitary method is:

  1. Aएक इकाई का मान ज्ञात करना
  2. Bसीधे अंतिम उत्तर लिखना
  3. Cदो राशियों को जोड़ना
  4. Dप्रतिशत निकालना

Explanation

The basic approach of the unitary method is finding the value of one unit first, and then using that as the basis for further calculation.

Question 10

Which is the most suitable teaching method for teaching the unitary method to Class 5-6 students?

  1. Aबाज़ार/दुकान जैसी वास्तविक स्थितियों (जैसे कॉपी-पेंसिल खरीदना) से गतिविधि कराना
  2. Bकेवल सूत्र याद कराना
  3. Cबिना उदाहरण के परिभाषा पढ़ाना
  4. Dबिना समझाए प्रश्न हल करने देना

Explanation

Real-life buying-and-selling situations that are familiar to children help them easily grasp the practical meaning of the unitary method.

Frequently Asked Questions

How many questions come from Unitary Method in REET?+

REET 2024 had 1-2 questions from this topic in the Maths section, both based on real everyday contexts.

What is the first step of the unitary method?+

First find the value of one unit, and then use that same basis to work out the value of the required quantity.

What's the difference between direct and inverse proportion?+

In direct proportion, both quantities increase and decrease together (like item-price), while in inverse proportion, one increases as the other decreases (like workers-time).

Is the unitary method limited to primary classes only?+

No, the concept of the unitary method starts in Classes 5-7 and becomes the foundation for higher-class topics like profit-loss, time-work and speed.

What's the most common mistake in the unitary method?+

The most common mistake is multiplying or dividing straight away without checking whether the given situation is direct or inverse proportion - this flips the answer completely.

Is the unitary method used only for finding price?+

No, it can be used for calculations involving any two related quantities besides price - such as time, distance, work, or weight.

What topics build on the unitary method later?+

It goes on to form the foundation of the calculation approach for practical topics like ratio-proportion, time-work, speed-distance-time, and profit-loss.

Does the unitary method always require division?+

No, division is used in the first step to find the unit value, but the second step - working out the required quantity - can use either division or multiplication.

What is the relationship between the unitary method and ratio-proportion?+

The unitary method is actually a practical form of ratio-proportion, in which the relationship between two quantities is solved by connecting it to the value of one unit.

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REET 2024 Solved Paper

Read all REET 2024 questions with solutions and explanations.

Official Sources

  1. NCERT Class 6-8 Maths textbooks (official)
  2. Rajasthan Board of Secondary Education (BSER) - official REET information

Change Log

  • 17 September 2026 — English page published — mirrors the fact-checked Hindi page, independently bilingual-accuracy checked