CLASS-7
PROPORTION - PROBLEM & SOLUTION

PROPORTION - PROBLEM & SOLUTION -

Example.1) Check whether the numbers 1.5, 2.5, 3.6, 6.0 are in proportion.

Ans.) Product of extremes = 1.5 × 6 = 9.0 Product of means = 2.5 × 3.6 = 9.0

By cross product rule, 1.5, 2.5, 3.6, 6.0 are in proportion.  (Ans.)

Example.2) Find the value of x in the proportion

           𝟏               𝟏           𝟏

       ------- : x = ------- : -------  

           𝟔               𝟐           𝟓

Ans.) Using cross product rule we get,

           𝟏                  𝟏            𝟏

       -------- : x =  -------- : --------  

           𝟔                  𝟐            𝟓      

          𝟏                 𝟏             𝟏

Or,  -------- ÷ x = -------- ÷ --------  

          𝟔                 𝟐             𝟓

          𝟏/6           𝟏/2            

Or,   -------- = --------- 

           x            𝟏/𝟓         

          𝟏           1           𝟏            

Or,  ------- x ------- = ------- X  x

          𝟔           5           𝟐       

          1            x

Or,  -------- = -------

          30           2

                   1

Or, x  =  --------- × 2

                  30

                   1

Or,    x = --------          (Ans.) 

                  15

To find out third or fourth proportional:-

Example.3) Find the third proportional to $4, $12.

Ans.) Let the third proportional be $x, then $4, $12 and $x are in continued proportion.

          4           12

Or,   ------- = -------

          12           𝑥

Or,     4x = (12 × 12)

               144

Or,    x = ------- = 36

                4

The third proportional is $36.        (Ans.)

Example.4) Find the fourth proportional to 1.5, 2.5, 4.5.

Ans.) Let the fourth proportional be x. Then, 1.5, 2.5, 4.5, x are in proportion.

Using cross product rule we get, 1.5 × x = 2.5 × 4.5

                 (2.5 × 4.5)

Or, x  = ------------------   

                      1.5

Or,  x = 7.5

Ans: The fourth proportional is 7.5    (Ans.)

Example.5) In a computer lab, there are 5 computers for every 8 students. How many computers will be needed for 40 students ?

Ans.) Let the number of computers needed be x.

Since the ratios are in proportion,

computers: students = 5 : 8 = x : 40.

                                        5            x

                                 => ------- = --------

                                        8           40

By cross product rule we get, 8x = 5 × 40

               200

Or,  x  = ---------  =  25

                8

The number of computers required = 25.   (Ans.)

Example.6) At a particular time, the shadow of a pole and a building are 1.7m and 7.3m respectively. If the height of the building is 21.9m, find the height of the pole.

Ans.) Let the height of the pole be x m.

Then, shadow of pole: building = height of pole : building

Or, 1.7: 7.3 =x : 21.9

            1.7          x

Or, ------- = --------

       7.3         21.9

By cross product rule, 7.3x = (1.7 × 21.9)

           (1.7 × 21.9)

Or, x = -------------

               7.3

Or, x = 5.1m.

The height of the pole is 5.1m.  (Ans.)

CONTINUED PROPORTION-

Three quantities a ,b and c of the same kind and in same units are said to be in continued

                                𝑎          𝑏

proportion if a:b=b:c, or, ------ = ------

                                𝑏          𝑐

or, b2=ac

Example.7) Check whether 7, 49 and 343 are in continued proportion or not.

Ans.) In order to be in continued proportion, 7 : 49 = 49 : 343

Product of means = 49 × 49 = 2401

Product of extremes = 7 × 343 = 2401

Since b2=ac, the numbers 7, 49 and 343 are in continued proportion.

7,49 and 343 are in continued proportion.   (Ans.)