Note on Unitary Method and Variation

  • Note
  • Things to remember
  • Exercise
  • Quiz

Unitary Method

The unitary method is a method, in which the value of a quantity is first obtained to find the value of any required quantity.

There are two types of variation while solving the problem of unitary method. They are

  • Direct variation
  • Inverse variation
.,

Direct Variation

When the increase or decrease in the value of one quantity causes the increase or decrease in the value of other quantity than they are said to be direct variation. For example, the cost of goods varies directly to the numbers of goods. More good, more cost. Less good, less cost.

Inverse Variation

When the increase or decrease in the value of one quantity causes the decrease or increase in the value of other quantity then they are said to be inverse variation. For example, time and work. More time consumes to complete a piece of work with less number of men's.

  • The Unitary Method provides an alternative approach to solving problems.
  • Percentages and simple percentage problems would normally precede the unitary method approach.
  • Ratio calculations are an aspect of the unitary method.
.

Very Short Questions

Solution:

12 men can make a furniture in 9 days.

1man can make it in 9 × 12 days = 108 days.

18 men can make the furniture in \(\frac{108}{18}\) days = 6 days

Solution:

Since 6 pens cost = Rs 450.

So, cost of 1 pens = Rs \(\frac{450}{6}\) = Rs 75

So, cost of 8 pens = Rs 75×8 = Rs 600

Solution:

10 Japanese Yen = Rs 6.60

1 Japanese Yen = Rs \(\frac{6.60}{10}\)

65,300 Japanese Yen = Rs \(\frac{6.60}{10}\)× 65300 = Rs 43,098

Solution:

10 Kg Oranges cost Rs 750

1 kg Orange cost Rs \(\frac{750}{10}\) = Rs 75

6 kg Oranges cost Rs 75×6 = Rs 450

∴ 6 kg Oranges cost Rs 450

Solution:

18 days is required to complete the work for 10 workers.

1 day is required to complete the same work for = 10×18 = 180 workers.

15 days is required to complete the work = \(\frac{180}{15}\) = 12 workers.

∴ 12 workers can do the same work in 15 days.

Solution:

Since, cost of 4 Computer chairs = Rs 1,544

So, cost of 1 Computer chairs = Rs \(\frac{1544}{4}\) = Rs 386

And cost of 14 Computer Chairs = Rs 386×14 = Rs 5,404

Solution:

In 10 days, a worker earns = Rs 1,850

In 1 day, a worker earns = Rs \(\frac{1850}{10}\) = Rs 185

In 3 days, a worker earns = Rs 185× 3 = Rs 555

Hence, he will earn Rs 555 in 3 days.

Solution:

Cost of 93m cloth = Rs 1395

Cost of 1m cloth = Rs \(\frac{1395}{93}\) Rs 15

Cost of 105m cloth = Rs 15×105 = Rs 1575

∴ The Cost of 105m cloth is Rs 1575

Solution:

If, 6 hours is required to finish the work for 4 men

1 hour is required to finish the work for 4×6 = 24 men

4 hours is required to finish the work for \(\frac{24}{4}\) = 6 men

∴ 6 men is required to finish the work in 4 hours.

Solution:

5 Euro = Rs 625

1 Euro = Rs \(\frac{625}{5}\) = Rs 125

Rs 8,946 = \(\frac{8,946}{125}\) = 71.568 Euro

Solution:

Since, Cost of 5 computer mouse = Rs1250.

So, Cost of 1 computer mouse = Rs \(\frac{1250}{5}\) = Rs 250

And Cost of 10 computer mouse = Rs 250×10 = Rs 2,500

∴ The cost of 10 computer mouse is Rs 2,500

0%
  • 4 computer chairs cost Rs 1544, find the cost of 14 computer chairs.

     

    Rs 5408
    Rs 5505
    Rs 5808
    Rs 5404
  • A workers earns Rs 1850 in 10 days. How much he will earn in 3 days?

     

    Rs 595
    Rs 355
    Rs 555
    Rs 565
  • If Sabina can travel 190 miles in 5 hours, how many miles she can travel for 7 days?

     

    6284 miles
    6375 miles
    6000 miles
    6384 miles
  • If 3 dozen bananas cost Rs 90, how many bananas can be bought for Rs 225 ?

     

    80
    60
    90
    70
  • If a car covers 48 km in 1 ltr of petrol, how many liters of petrol are required to cover a distance of 432 km?

     

    5 liters
    9 liters
    10 liters
    8 liters
  • 12 men dig a pond in 8 days. How many men can dig it in 6 days?

     

    20 men
    12 men
    16 men
    15 men
  • 4 people can finish a piece of work in 6 hours. How many can do it in 4 hours?

     

     8 people
     10 people
     15 people
     6 people
  • If 36 men can do a piece of work in 25 days, in how many days can 15 men do it?

     

      45 days
      30 days
      69 days
      60 days
  • A student working 8 hours a day takes 5 days to complete a project. How many hours a day must he work to complete it in 4 days?

     

    12hours
    8 hours
    5 hours
    10 hours
  • Sunita types 450 words in half an hour. How words would she type in 7 minutes?

    110 words
    95 words
    90 words
    105 words
  • A train is moving at a uniform speed of 68 km per hour. How far will it go in 15 minutes?

    17 km
    25 km
    20 km
    15 km
  • 12 tailors can stitch 15 shirts in a day. How many shirts will be stitched by 28 tailors in a day?

    10 shirts
    30 shirts
    25 shirts
    35 shirts
  • In 8 hours, workers fill 960 bottles of cold drinks. How many bottles will be filled in 6 hours.

    710 bottles
    725 bottles
    820 bottles
    720 bottles
  • Sanjay types 57 words in 3 minutes. How many words would he type in 1 hour?

    1150 words
    1240 words
    1140 words
    2140 words
  • The weight of 56 books is 7 kg. What is the weight of 90 such books?

     

     

    ;i:2;s:15:
    ;i:1;s:15:
    ;i:3;s:15:
    ;i:4;s:12:
  • You scored /15


    Take test again

DISCUSSIONS ABOUT THIS NOTE

You must login to reply

Forum Time Replies Report


You must login to reply


You must login to reply


You must login to reply

A pen cost is RS12.Find the cost of 12 pens


You must login to reply