Unitary Method | Math | Chapter 8 | Grade 5 | With Exercises Solution

Unitary Method

Objectives:

Student will be able to:

1. Understand the methods of determining the total value from the unit value.
2. Determine the unit value from the total values provided the number items.

Outcomes:

Students will have learnt to use their understanding on unitary methods on their day to day dealings.

Materials:

Multiplication chart, different items with tags, bills, price list, etc.

Unitary Methods/button

Question: What is Unitary Method?
Answer: The mathematical method used to find out the unit value or the value of any given number of quantities is known as the unitary method. alert-info

If we are given the value of an item (unit) then we can find the total value for the given number of items. Similarly, if we are given the values of total number of items, we can find the value for a single (unit) item.

Also Check:

Easy ways for Testing Divisibility | Divisibility Rules.
Geometry | Math | Chapter 1 | Grade 5 | With Exercises Solution
The Number System | Math | Chapter 2 | Grade 5 | With Exercises Solution
Prime and Composite Numbers | Math | Chapter 3 | Grade 5 | With Exercises Solution
Fundamental Operations | Math | Chapter 4 | Grade 5 | With Exercises Solution
Measurement System | Math | Chapter 5 | Grade 5 | With Exercises Solution
Mensuration | Math | Chapter 6 | Grade 5 | With Exercises Solution
Unitary Method | Math | Chapter 8 | Grade 5 | With Exercises Solution
Profit and Loss | Math | Chapter 9 | Grade 5 | With Exercises Solution
Simple Interest | Math | Chapter 10 | Grade 5 | With Exercises Solution
Sets | Math | Chapter 13 | Grade 5 | With Exercises Solution
Algebra | Math | Chapter 14 | Grade 5 | With Exercises Solution

For example: If the price of a pencil is given, we can easily find the total price of any number of pencils. Similarly, if the price for certain number of pencils are given, we can find the price for a single pencil.

Things to remember:

Vocabulary:
Unitary - एकात्मक, method - विधि, quantity - मात्रा, परिणाम, interest - व्याज, average - औसत, सरदर. alert-info

Unit price would be less, so there will be division for a unit item. Total price for a given quantity will be more, so there will be multiplication for a given quantity. alert-info

Grade 5: Math Subject-Chapter:8 - Unitary Method: Exercise 8.1 (With Solution)/button

1. The unit price for a copy is Rs. 15. Find the cost for the following items.

a. one copy
Solution:
Here,
unit price (1 copy) = Rs. 15
No. of copy = 1
We know that,
Total price = unit price x No. of copy = Rs. 15 x 1 = Rs. 15.
Therefore, the price of one copy is Rs. 15.

b. 5 copies
Solution:
Here,
unit price (1 copy) = Rs. 15
No. of copy = 5
We know that,
Total price = unit price x No. of copy = Rs. 15 x 5 = Rs. 75.
Therefore, the price of one copy is Rs. 75.

c. 6 copies
Solution:
Here,
unit price (1 copy) = Rs. 15
No. of copy = 6
We know that,
Total price = unit price x No. of copy = Rs. 15 x 6 = Rs. 90.
Therefore, the price of one copy is Rs. 90.

d. 8 copies
Solution:
Here,
unit price (1 copy) = Rs. 15
No. of copy = 8
We know that,
Total price = unit price x No. of copy = Rs. 15 x 8 = Rs. 120.
Therefore, the price of one copy is Rs. 120.

e. one dozen copies
Solution:
Here,
unit price (1 copy) = Rs. 15
No. of copy (1 dozen copies) = 12
We know that,
Total price = unit price x No. of copy = Rs. 15 x 12 = Rs. 180.
Therefore, the price of one copy is Rs. 180.

f. 5 dozens of copies
Solution:
Here,
unit price (1 copy) = Rs. 15
1 dozen copies = 12 copies.
So, 5 dozens copies = 12 x 5 = 60 copies.
No. of copy (1 dozen copies) = 60 copies
We know that,
Total price = unit price x No. of copy = Rs. 15 x 60 = Rs. 900.
Therefore, the price of one copy is Rs. 900.

2. If a banana cost Rs. 3, find the cost of a dozen of bananas?
Solution:
Here,
Unit price = Rs. 3
1 dozen bananas = 12 bananas
So, No. of bananas = 12
We know that,
Total price = unit price x No. of bananas = Rs. 3 x 12 = Rs. 36.
Therefore, the price of 3 bananas is Rs. 36.

3. If a dozen of eraser costs Rs. 24, find the cost of:
a. one eraser, b. 3 erasers, c. 6 erasers.
Solution:
Here,
Total costs of erasers = Rs. 24
Number of erasers = 1 dozens erasers = 12 erasers.
Unit price = ?
We know that,
Unit cost/price = Total cost/No. of erasers = Rs. 24/12 = Rs. 2.
Therefore, the cost of one eraser is Rs. 2.

b. 3 erasers
Solution:
Here,
Total costs of erasers = Rs. 24
Number of erasers = 1 dozens erasers = 12 erasers.
Unit price = ?
We know that,
Unit cost/price = Total cost/No. of erasers = Rs. 24/12 = Rs. 2.
Therefore, the cost of one eraser is Rs. 2.
Hence, the cost of 3 erasers = 3 x Rs. 2 = Rs. 6.

c. 6 eraser
Solution:
Here,
Total costs of erasers = Rs. 24
Number of erasers = 1 dozens erasers = 12 erasers.
Unit price = ?
We know that,
Unit cost/price = Total cost/No. of erasers = Rs. 24/12 = Rs. 2.
∴ the cost of one eraser is Rs. 2.
Hence, the cost of 6 erasers = 6 x Rs. 2 = Rs. 12.

4. Ujjwal went to shopping. The shopkeeper said that the cost for a dozen of pair shocks cost Rs. 840. How much money should he spend to buy 6 pairs of shocks?
Solution:
Here,
Total costs of dozen of pairs shocks = Rs. 840
Number of pair shocks = 1 dozens pair shocks = 12 pair shocks.
Unit price = ?
We know that,
Unit cost/price = Total cost/No. of pair shocks = Rs. 840/12 = Rs. 70.
∴ the cost of a pair of shocks is Rs. 70.
Hence, the cost of 6 pair of shocks is 6 x Rs. 70 = Rs. 420.

5. Rupesh earns Rs. 500 in a day? How much does he earn in a month?
Solution:
Here,
In a day, Rupesh earns = Rs. 500
1 month = 30 days
∴ Total earnings in a month = Earnings in a day x Total days = Rs. 500 x 30 = Rs. 15,000.

6. A man walks 21 km in 3 hours. How long does he take to walk 35 km?
Solution:
Here,
A man walks 21 km in 3 hrs.
So, a man walks 1 km in 3/21 hrs.
Now,
∴ A man walks 35 km in 3/21 x 35 hrs = 5 hours.

7. A car moves 80 km in an hour. How far does it move in 5 hours?
Solution:
Here,
In an hour, a car moves 80 km.
∴ In 5 hours, a car moves 5 x 80km = 400 km.

8. A bus moves at an average speed of 50 km per hour. The distance between Pokhara and Kathmandu is 200 km. How long does a bus take to make a trip from Pokhara to Kathmandu?
Solution:
Here
A bus moves 50 km in an hour.
A bus moves 1 km in 1/50 hrs.
A bus moves 200 km in 1/50 x 200 hrs = 4 hrs.
∴ a bus takes 4 hrs to make a trip from Pokhara to Kathmandu.

9. A motorcycle runs 160 km on 4 litres of petrol. How far it will go with 7 liters of petrol?
Solution:
Here,
With 4 liters of petrol, a motorcycle runs 160 km.
With 1 liter of petrol, a motorcycle runs 160/4 km.
∴ With 7 liters of petrol, a motorcycle runs 160/4 x 7 = 280 km.

10. 6 televisions cost Rs. 1,20,000. What is a cost of a television? If Ajay wants to buy 3 televisions, how much money does he need to spend?
Solution:
Here,
6 televisions cost Rs. 1,20,000.
1 television costs Rs. 1,20,000/6.
Ajay wants to by 3 televisions.
So, 3 televisions cost Rs. 1,20,000/6 x 3 = Rs. 60,000.
∴  Ajay needs to spend Rs. 60,000 to buy 3 televisions.

11. The cost of 5 kg of rice is Rs. 250. How much rice can be bought for Rs. 600?
Solution:
Here,
In Rs. 250, we can buy rice of 5 kg.
In Re. 1, we can buy rice of 5/250 kg.
In Rs. 600, we can buy rice of 5/250 x 600 = 12 kg.
∴  12 kg of rice can be bought for Rs. 600.

12. There are two items mustard oil (5 packets - Rs. 120, Rs. 120, Rs. 120, Rs. 120, Rs. 120) and sunflower oil (4 packets - Rs. 140, Rs. 140, Rs. 140, Rs. 140). Which item needs more money and by how much?
Solution:
Here,
1 packet of mustard oil costs = Rs. 120.
5 Packets of mustard oil cost = Rs. 120 x 5 = Rs. 600.
And,
1 packet of sunflower oil costs = Rs. 140.
4 packets of sunflower oil cost = Rs. 140 x 4 = Rs. 560.
So, Mustard oil needs more money.
∴  Mustard oil needs Rs. 600 - Rs. 560 = Rs. 40 more money.

13. One dozen of eggs cost Rs. 108. Find the cost of 16 eggs.
Solution:
Here,
One dozen = 12
So, 12 eggs cost Rs. 108.
1 egg cost Rs. 108/12 = Rs. 9.
So, 16 eggs cost Rs. 9 x 16 = Rs. 144.

14. The simple interest on Rs. 100 for 1 year is Rs. 12. Calculate the interest on Rs. 600 for 1 year.
Solution:
Here,
Interest on Rs. 100 for 1 year = Rs. 12
∴ Interest on Rs. 1 for 1 year = Rs. 12/100
∴ Interest on Rs. 600 for 1 year = Rs. 12/100 x 600 = Rs. 72.

15. If the simple interest on Rs. 100 for 1 year is Rs. 9, calculate the interest on Rs. 400 for 4 years.
Solution:
Here,
Interest on Rs. 100 for 1 year = Rs. 9
∴ Interest on Rs. 1 for 1 year = Rs. 9/100
∴ Interest on Rs. 400 for 1 year = Rs. 9/100 x 400
∴ Interest on Rs. 400 for 4 years = Rs. 9/100 x 400 x 4 = Rs. 144.

16. Which one earns more interest?
i) Rs. 900 at 6% per annum in 2 years, or
ii) Rs. 700 at 8% per annum in 3 years.
Solution:
i) Here,
Principle (P) = Rs. 900
Interest Rate (R) = 6%
Time (T) = 2 years
We know that,
Interest = PTR/100 = Rs. 900 x 2 x 6% = Rs. 900 x 2 x 6/100 = Rs. 108.

ii) Here,
Principle (P) = Rs. 700
Interest Rate (R) = 8%
Time (T) = 3 years
We know that,
Interest = PTR/100 = Rs. 700 x 3 x 8% = Rs. 700 x 3 x 8/100 = Rs. 168.
∴ No. ii) Rs. 700 at 8% per annum in 3 years earns more interest.

Cumulative Test-7, Unitary Method - Solution/button

1. The cost of 5 pencils is Rs. 50, what is the cost of 1 pencil?
Solution:
Here,
Costs of 5 pencils = Rs. 50
∴ Cost of 1 pencil = Rs. 50/5 = Rs. 10.
∴ The cost of 1 pencil is Rs. 10.

2. The cost of book is Rs. 250, what is the cost of 4 books?
Solution:
Here,
The cost of a book = Rs. 250
∴ The cost of 4 books = Rs. 250 x 4 = Rs. 1,000.
∴ The cost of 4 books is Rs. 1,000.

3. The cost of one dozen of banana is Rs. 75. What is the cost of one banana?
Solution:
Here,
The cost of one dozen banana = Rs. 75
∴ The cost of 12 bananas = Rs. 75
∴ The cost of 1 banana = Rs. 75/12 = Rs. 6.25.
∴ The cost of one banana is Rs. 6.25.

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