PRACTICE QUESTIONS ON DIRECT AND INVERSE PROPORTION

Question 1 :

A man white washes 96 sq.m of a compound wall in 8 days. How many sq.m will be white washed in 18 days?

Solution :

Let x be square meters white washed in 18 days.

         Area                   Number of days

96                              8 

x                              18 

If we have more number of days, then we will white wash more area. So, it is in direct variation.

96 ⋅ 18  =  8 ⋅ x

x  =  (96 ⋅ 18)/8

x  =  1728/8

x  =  216 sq.m

So, the man will white wash 216 sq.m.

Question 2 :

7 boxes weigh 36.4 kg. How much will 5 such boxes weigh?

Solution :

Let x be the weight of 5 such boxes.

             Number of boxes                    Weight of boxes 

                     7                                            36.4

                     5                                             x

If the number of boxes are reducing, then its weight will also decrease. So, it is direct variation.

7 ⋅ x = 5 ⋅ 36.4

x  =  (5 ⋅ 36.4)/7

x  =  182/7

x  =  26 kg

So, the weight of 5 boxes is 26 kg.

Question 3 :

A car takes 5 hours to cover a particular distance at a uniform speed of 60 km/hr. How long will it take to cover the same distance at a uniform speed of 40 km/hr ?

Solution :

Let x be the distance covered at a uniform speed of 40 km/hr.

Speed                           Time taken 

60                                     5

40                                      x 

The speed is decreasing, then the time taken to cover the same distance will increase. So, it is in inverse variation.

60 ⋅ 5  =  40 ⋅ x

x  =  (60 ⋅ 5)/40

x  =  300/40

x  =  7.5 hours

So, the car will take 7.5 hours to cover the same distance.

Question 4 :

150 men can finish a piece of work in 12 days. How many days will 120 men take to finish the same work?

Solution :

Let x be the required number of days taken to finish the work.

           Number of men                      Number of days 

                 150                                            12 

                 120                                            x

Number of men is decreasing, so the number of days will increase. This is in inverse variation.

150 ⋅ 12  =  120 ⋅ x

x  =  (150 ⋅  12)/120

x  =  1800/120

x  =  15 days

So, 120 men will take 15 days to complete the same work.

Question 5 :

A troop has provisions for 276 soldiers for 20 days. How many soldiers leave the troop so that the provisions may last for 46 days? 

Solution :

Let x be the required number of soldiers.

 Number of soldiers                   Number of days

276                                       20 days

x                                         46 days

Since the number of days is increasing then number of soldiers will decrease. This is in inverse variation.

276 ⋅ 20  =  x ⋅ 46

x  =  (276 ⋅ 20)/46

x  =  5520/46

x  =  120

So, 120 solders will use provision for 46 days.

Question 6 :

A book has 70 pages with 30 lines of printed matter on each page. If each page is to have only 20 lines of printed matter, how many pages will the book have?

Solution :

Let x be the number of pages

Number of pages                    Number of lines

70                                       30 lines

x                                         20 lines

Here 70 pages is containing 30 lines. If the number of lines is decreasing then number of pages will increase. So it is in inverse variation.

70 ⋅ 30  =  20 ⋅ x

x  =  (70 ⋅30)/20

x  =  2100/20

x  =  105 pages 

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