## Chapter 1 Simplification Unitary Method

## Unitary Method :

- The unitary method is a method of solving a problem by obtaining the value of one unit of material from some given value of the material.
- Suppose you are given that the cost of 10 pens is 50. You have to obtain the cost of 16 pens.
- Here we have to find the cost of one pen, then find the total cost of 16 pens.
- So the cost of 10 pens = 50
- ∴ The cost of 1 pen = ₹ \(\frac{50}{10}\) = 5
- (Here the number of pens is less, so the cost would be less.
- Therefore, the division process must be done.)
- ∴ The cost of 16 pens = ₹ (5 x16) = ₹ 80.
- (Here the number of pens is more, so the cost would be more. Therefore, the multiplication process must be done.)
- Similarly, if the cost of 5 apples is 30, then what is the cost of 12 apples?
- So to solve this problem, we can take the help of the above unitary method.
- Here cost of 5 apples = ₹ 30
- ∴ Cost of 1 apple = ₹ \(\frac{30}{5}\) =₹ 6
- So the cost of 12 apples = 6 x 12 = ₹ 72.
- In general, two variables are so related that if one variable increases which cause, the increase of the other variable, or the decrease of one variable causes the decrease of the other variable, then the relation is said to be direct relation.
- On the other hand, if the increase of one variable causes the decrease of the other variable or the decrease of one variable causes the increase of the other variable, then the relation between the variable is said to be indirect relation or inverse relation.
- For example, the number of books is variable and the cost of the books is another variable.
- There exists a direct relation between these two variables.
- This means that the increase in the number of books causes an increase in the cost of the books or the decrease in the number of books causes a decrease in the total cost of the books.
- The relation between the variable is direct.
- Again let us consider that some men complete work in some days.
- Here for the same amount of work done the number of days required is a variable and the number of men required is the other variable.
- For the same amount of work, if the number of men is more they would take less number of days to finish the work.
- Also if the number of men is less then they would take more days to finish the work.
- The relation between the variables is indirect or inverse.
- The relation between the number of books and their cost is a direct relation i.e., the increase in the number of books causes an increase in their cost and the decrease in the number of books causes a decrease in their total cost.
- On the other hand, the relation between the number of daily working hours to complete work and the number of days required is inverse relation, i.e., the increase in the daily working hours causes the decrease in the number of days required to complete the work and the decrease of the daily working hours causes the increase of the number of days required to complete the work.

**class 6 math wbbse solution**

**So there exist two variables in general two relations: **

- Direct Relation
- Indirect or Inverse Relation.

For direct relation, the value of unit quantity would be less and for inverse relation, the value of unit quantity would be more.

To solve this type of problem, first, you have to ascertain which type of relationship exists between the variables, then solve the problem using the unitary method otherwise the wrong results may come.

You observe the following worked-out examples, then you will have a clear concept or idea about the unitary method.

**Class 6 West Bengal Board Math Solution**

**Question 1. If 40 laborers can take 35 days to construct a part of the embankment of the Matla River, then how many laborers will be required to construct the same part of the bank in 28 days?**

**Solution:**

**Given:**

40 laborers can take 35 days to construct a part of the embankment of the Matla River

A part of the embankment of the Matla River can be constructed in 35 days by 40 laborers.

∴ The same part can be constructed in 1 day by 40 x 35 laborers.

∴ In 28 days the same part can be constructed by

laborers

= (10 × 5) = 50 labourers

∴ 50 laborers can be required.

**Question 2. Debarsi, Debalina, Debmalya, and Debdut can do 150 sums in 6 days. If each of them can do a same number of sums per day, then how many days will be required to do 250 sums by Debarsi and Debalina?**

Solution :

**Given**:

Debarsi, Debalina, Debmalya, and Debdut can do 150 sums in 6 days. If each of them can do a same number of sums per day

Here total number of men = 4, the number of days = 6, and the number of sums = 150.

It is also given that each of them can do every day a same number of sums.

So, 4 persons can do 150 sums in 6 days

1 person can do 150 sums in 6 x 4 = 24 days

1 persons can do 150 sums in \(\frac{24}{150}\)

2 persons can do 1 sums in \(\frac{24}{150 x 2}\) day

∴ 2 persons can do 250 sums in

days = 2 x 10 = 20 days

∴ The total number of required days = 20.

**Read And Learn More: WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Solved Problems**

**Question 3. 45 laborers can dig a well in 24 days. If the well can be dug in 18 days, then how many more laborers will be required?**

**Solution: **

**Given:**

45 laborers can dig a well in 24 days. If the well can be dug in 18 days

A well can be dug in 24 days by 45 laborers.

∴ The well can be dug in 1 day by 45 x 24 laborers.

The well can be dug in 8 days by

= 60 laborers.

There are already 45 laborers.

∴ 60 – 45 = 15 more laborers will be appointed.

**Class 6 West Bengal Board Math Solution**

**Question 4. : If 2 men can polish \(\frac{1}{3}\) ****part of a table in one day, then how many men will be required to polish \(\frac{2}{3}\) ****part of the table in 2 days?**

**Solution :**

**Given:**

2 men can polish \(\frac{1}{3}\) part of a table in one day

\(\frac{1}{3}\) part of a table can be polished in 1 day by 2 men

∴ 1 part of the table can be polished in 1 day by 2 x \(\frac{3}{1}\) men

∴ 1 part of the table can be polished in 2 days by \(\frac{2 \times 3}{1 \times 2}\)

\(\frac{2}{3}\) part of the table can be polished in 2 days by \(\frac{2 \times 3}{1 \times 2} \times \frac{2}{3}\)

∴ The required number of men = 2.

**Question 5. 175 kg of rice is required for a week for a mid-day meal of 500 students. After 75 kg of rice has been used, how long will the remaining rice last for 400 students?**

**Solution:**

**Given:**

175 kg of rice is required for a week for a mid-day meal of 500 students. After 75 kg of rice has been used

One week 7 days.

Amount or remaining rice = (175 – 75) kg = 100 kg.

175 kg of rice will last 500 students for 7 days

1 kg of rice will last for 500 students for \(\frac{7}{175}\) days

1 kg of rice will last for 1 student for \(\frac{7 \times 500}{175}\) days

100 kg of rice will last for 1 student for \(\frac{7 \times 500}{175} \times 100\) days

100 kg of rice will last 400 students for

Days = 5 days

The remaining rice will last for 400 students for 5 days.

**Class 6 West Bengal Board Math Solution**

**Question 6. If the price of 15 books is 1275, then how many books will be purchased for 2125?**

**Solution:**

**Given:**

The price of 15 books is 1275

For₹ 1275, the number of books purchased = is 15

For ₹ 1, the number of books be purchased = \(\frac{15}{1275}\)

For ₹ 2125, the number of books be purchased = \(\frac{15 \times 2125}{1275}\)

∴ The required number of books = is 25.

**Question 7. Sita, Gita, and Rita can complete a piece of work separately in 12 hours, 15 hours, and 18 hours respectively. If they do it together then in how many hours will they complete \(\frac{1}{2}\)of the work?**

**Solution:**

**Given:**

Sita, Gita, and Rita can complete a piece of work separately in 12 hours, 15 hours, and 18 hours respectively.

Here the whole of the work = 1 part.

Then Sita can complete the work in 12 hours.

∴ Sita in 12 hours, can do 1 part of the work In 12 hours, Sita can do 1 part of the work

∴ In 1 hour, Sita can do \(\frac{1}{12}\) part of the work.

Gita can do in 15 hours 1 part of the work.

In 1 hour, Gita can do \(\frac{1}{15}\) part of the work.

In 18 hours, Rita can do 1 part of the work.

∴ In 1 hour, Rita can do \(\frac{1}{18}\) part of the work.

So in 1 hour Sita, Gita, and Rita together can do (\(\frac{1}{12}\) + \(\frac{1}{15}\) + \(\frac{1}{18}\) part of the work

= \(\frac{15 + 12 + 10}{180}\) part

= \(\frac{37}{180}\) part of the work.

∴ Sita, Gita, and Rita together can do \(\frac{37}{180}\) part of the work in 1 hour.

∴ Sita, Gita, and Rita together can do 1 part of the work in \(\frac{1 \times 180}{37}\) hours

They together can do \(\frac{1}{2}\) part of work in \(\frac{1 \times 180}{2 \times 37}\) hours

= \(\frac{90}{37}\) hours = 2 \(\frac{16}{37}\) hours.

∴ The required time = 2 \(\frac{16}{37}\)hours.

**Wbbse Class 6 Maths Solutions**

**Question 8. : 4 tractors are required to cultivate 360 bighas of land in 20 days. How many tractors will be required to cultivate 1800 bighas of land in 10 days? **

**Solution:**

**Given:**

4 tractors are required to cultivate 360 bighas of land in 20 days.

To cultivate 360 bighas of land in 20 days 4 tractors are required.

**Question 9. There are 20 boys in a hostel and 150 kg of atta is stored for them for 30 days. But 30 kg of atta was wasted and 5 boys went home from the hostel. How long will the remaining boys be fed with the remaining amount of atta?**

**Solution:**

**Given:**

There are 20 boys in a hostel and 150 kg of atta is stored for them for 30 days. But 30 kg of atta was wasted and 5 boys went home from the hostel.

The total amount of atta stored in the hostel was 150 kg and the amount of atta wasted was 30 kg.

∴ Remaining amount of atta= (150 – 30) = 120 kg

The remaining number of boys in the hostel = is 20 – 5 = 15.

In mathematical language, we have

**Wb Class 6 Maths Solutions**

**Question 10. 15 vans can carry 75 quintals of fish in 40 minutes. How long will 20 vans carry 100 quintals of fish?**

**Solution:**

**Given:**

15 vans can carry 75 quintals of fish in 40 minutes.

In mathematical language, we have,

**Wb Class 6 Maths Solutions**

**Question 11. 12 farmers can cultivate land in 7 days working 6 hours a day. How many farmers will be required to cultivate that land in 9 days working 4 hours a day?**

**Solution:**

**Given:**

12 farmers can cultivate land in 7 days working 6 hours a day.

In mathematical language, we have,

**Question 12. A compositor can compose 11 pages in 8 hours. How many days will be required to compose a book containing 264 pages working 6 hours on average per day?**

**Solution:**

**Given:**

A compositor can compose 11 pages in 8 hours

In mathematical language, we have,

**Wb Class 6 Maths Solutions**