# Direct And Inverse Proportions Questions

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#### List of direct and inverse proportions Questions

Question NoQuestionsClass
1The cube root of ( x ) varies inversely as the square of y. If ( x=8 ) when ( y=3 ), then find ( mathbf{x} ) when ( boldsymbol{y}=mathbf{1} frac{mathbf{1}}{mathbf{2}} )8
2( x ) ( begin{array}{ccccc}mathbf{2} & mathbf{3} & mathbf{5} & mathbf{6} & mathbf{1 0} \ 15 & 10 & b & 5 & 3end{array} ) ( y )
Identify the inverse proportional
quantities.
( mathbf{A} cdot 4 )
B. 5
( mathbf{c} cdot mathbf{6} )
D. 10
8
357. If x: y = 3:4, then
4x + 5y: 5x – 2y =
(1) 7: 32 (2) 32:7
(3) 4:3 (4) 5 : 2
8
4If ( a ) is inversely proportional to ( b ) and ( b )
is inversely proportional to ( c ) then what
is proportionality between ( a ) and ( c ? )
A. Direct
B. Inverse
c. No proportionality
D. can’t be determinal
8
5Which of the following is an example of indirect proportion?
A. Number of mangoes in a bag and weight of the bag.
B. Earning and hours worked.
c. More the speed, lesser the time taken
D. None of these.
8
6A car travels ( 40 mathrm{km} mathrm{s} ) in 30 mins. If the
speed of bus remains same, how far can
it travel in 3 hrs?
A. ( 120 mathrm{km} )
B. ( 80 mathrm{km} )
( c .240 k m )
D. None of these
8
759. If x varies inversely as (y – 1)
and is equal to 24 when y = 10,
then the value of x when y=5 is
(1) 99
(2) 12
(3) 24
(4) 100
8
855 cows can graze a field in 16 days. How many cows will graze the same field in 10 days?8
9Mark the correct alternative of the
following.

If six men can do a piece of work in 6
days, then 3 men can do same work in?
A. 10 days
B. 12 days
c. 15 days
D. 18 days

8
10Find the value of ( x ) if ( a ) and ( b ) are in
direct proportion
( begin{array}{ccccc}a & 2 & 3 & 4 & 5 \ b & 14 & 21 & x & 35end{array} )
A . 16
в. 25
c. 27
D. 28
8
11Share of ( A, B ) and ( C ) respectively, are
if Rs. ( mathbf{5 4 6 0} ) is divided in ( frac{1}{2}: frac{1}{3}: frac{1}{4} )
A . Rs. 1680 , Rs. 2520 , Rs. 1260
B. Rs. 2520, Rs. 1680, Rs. 1260
c. Rs. ( 1260, ) Rs. ( 2100, ) Rs. 2520
D. Rs. ( 2520, ) Rs. ( 1260, ) Rs. 1680
8
121200 men can finish a stock of food in
35 days. How many more men should
join them so that the same stock may
last for 25 days?
8
13If y varies inversely with the fourth root
of ( x, ) and ( y=4 ) when ( x=frac{1}{16}, ) then what
is the value of ( y ) when ( x=frac{1}{81} )
8
14If ( x ) and ( y ) vary inversely as each other, and ( x=10 ) when ( y=6 . ) Find ( y ) when
( boldsymbol{x}=mathbf{1 5} )
A . 2
B. 4
c. 8
D.
8
1552. The prices of a school bag and a
shoe are in the ratio 7:5. The
price of a school bag is
200 more than the price of a
shoe. Then the price of a shoe is
(1) 200 (2) 700
(3) 500 (4) 1,200
8
16Suppose 2 kg of sugar contains 9106
crystals. How many sugar crystals are there in (i) 5 kg of sugar?
(ii) ( 1.2 mathrm{kg} ) of
sugar?
8
17If 30 men can reap a field in 14 days, in
how many days will 20 men reap it?
8
18Which of the following are in inverse proportion?
(i) The number of workers on a job and the time to complete the job.
(ii) The time taken for a journey and the distance travelled in a uniform speed.
(iii) Area of cultivated land and the crop
harvested.
(iv) The time taken for a fixed journey and the speed of the vehicle.
(v) The population of a country and the area of land per person.
8
19Which is an example of inverse
proportion?
A. More amount of sweets, more total cost
B. More length of cloth, more cost
C. More expenditure, less saving
D. More height of object, more length of its shadow
8
20A farmer has enough food to feed 28 animals in his cattle for 9 days. How long would the food last if there were 8
more animals in his cattle ?
A . 5
B. 7
c. 10
D. None of these
8
21The cost of 3 digital cameras and 5 cell phones is Rs. ( 35,290 . ) What is the cost of 9 digital cameras and 15 cell phones?
A . Rs. 1,68,450
B. Rs. 1,79,220
c. Rs. 1,05,870
D. None of these
8
22Four angles of a quadrilateral are in the ratio ( 3: 5: 7: 9 . ) The greatest angle is
A . ( 125^{circ} )
B . ( 75^{circ} )
( mathbf{c} cdot 135^{circ} )
D. ( 120^{circ} )
8
2358. In a mixture of 25 litres, the ra-
tio of acid to water is 4: 1. An-
other 3 litres of water is added
to the mixture. The ratio of acid
to water in the new mixture is
(1) 5:2 (2) 2:5
(3) 3:5 (4) 5:3
8
24A 5 m ( 60 mathrm{cm} ) high vertical pole casts a
shadow ( 3 m 20 mathrm{cm} ) long. Find at the
same time (i) the length of the shadow cast by another pole 10 m ( 50 mathrm{cm} ) high
(ii) the height of a pole which casts a shadow 5 m long.
8
25If 18 pumps can raise 2170 tonnes of
water in 10 days, working 7 hours a day then in how many days will 16 pumps raise 1736 tonnes of water, working 9 hours a day?
( A cdot 6 )
B. 7
( c cdot 8 )
D.
8
26Which of the following is the example of
direct proportion?
A. Number of mangoes in a bag and weight of the bag.
B. Speed goes up, travel times goes down
c. More the number of men lesser the time taken to complete it.
D. None of these.
8
27At a party, 8 bottles of soft drink are
served for every batch of 5 children. How
many bottles would be served if 40
children were present at the party?
8
28A stone is dropped into a well and the report of the stone striking the bottom is heard 7.7 seconds after it is dropped.
Assume that the stone falls ( 16 t^{2} m ) in ( t )
seconds and that the velocity of sound
is 1,120 per second. The depth of the well is:
( mathbf{A} cdot 784 mathrm{m} )
в. ( 342 mathrm{m} )
( c .1568 mathrm{m} )
D. ( 156.8 mathrm{m} )
E. none of these
8
29A work is done by 10 workers in 6 hours? How many workers will be required to do the same work in 4 hrs?
A . 10
B . 15
c. 20
D. None of these
8
30If the thickness of a pile of 12 cardboards is ( 35 mathrm{mm} ), find the thickness of a pile of 294 cardboards.8
31A worker is paid Rs 200 for 8 days work. If he works for 20 days, how much will
he get?
8
32Following are the car parking charges near railway station upto
( 4 mathrm{hrs} quad ) Rs 60
( mathbf{8} ) hrs ( quad boldsymbol{R} boldsymbol{s} mathbf{1 0 0} )
( mathbf{1 2} ) hrs ( quad boldsymbol{R} boldsymbol{s} mathbf{1 4 0} )
( mathbf{2 4} ) hrs ( quad boldsymbol{R} boldsymbol{s} mathbf{1 8 0} )
Check if the parking charges are in direct proportion to the parking time.
8
33The number of workers increased the
days to complete the work decreased.”is
example of
A. Inverse ratio
B. Direct ratio
C. Both of A and B
D. none of above
8
34A worker is paid Rs 210 for 6 days work. If his total income of the month is Rs
( 875, ) for how many days did he work?
8
35If the cost of ( 93 mathrm{m} ) of a certain kind of
plastic sheet is Rs ( 1395, ) then what would it cost to buy ( 105 mathrm{m} ) of such plastic sheet?
8
36Which of the following are in inverse
proportion?
This question has multiple correct options
A. The number of workers on a job and the time to complete the job.
B. The time taken for a journey and the distance travelled in a uniform speed.
C. Area of cultivated land and the crop harvested.
D. The time taken for a fixed journey and the speed of the vehicle.
E. The population of a country and the area of land per person.
8
37A bus travels ( 120 mathrm{km} ) in 4 hrs The distance that can be travelled by the
bus in 6 hrs is ( _{-} )
( mathbf{A} cdot 18 mathrm{km} )
B. 140 km
( c .180 mathrm{km} )
D. 120 km
8
38A man gets ( R s .7920 ) for working 48
hours a week. How much does he get
when he works 36 hours a week?
A. ( R s .7150 )
в. ( R s .5940 )
c. ( R s .6660 )
D. Rs. 4000
8
39In a Television game show, the prize money of Rs 1,00,000 is to be divided equally amongst the winners. Complete the following table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners??
Number of
winners
Prize of each
1,00,000
50,000
winner (in Rs)
8
4055. Three taps A, B and C can fill a
tank in 12, 15 and 20 hours re-
spectively. IfA is open all the time
and B and C are open for one
hour each alternatively, the tank
will be full in :
(1) 6 hours
(2) 6
hours
(3) 7 hours (4) 7 hours
8
41A car can finish a certain journey in 10 hours at the speed of ( 48 mathrm{km} / mathrm{hr} ). By how much should its speed be increased so that it may take only 8 hours to cover
the same distance ? (in km/hr)
8
4253.
If A: B= 2:1 and A: C= 1:3,
then A:B:C is
(1) 1:3:2 (2) 1:2:6
(3) 3:2:1 (4) 2:1:6
8
43A fist with a mass of 3 kg causes a
fishing pole to bend ( 9 mathrm{cm} . ) If the amount
of bending varies directly as the mass, how much will the pole bend for a ( 2 k g ) fish ?
8
44f ( 20: 28=x: 7=10: y )
The values of ( x ) and ( y ) in the box
respectively are
A .5,14
в. 14,5
( c .8,10 )
D. 10,8
8
4563. Pipes P and 9 can fill a tank in
10 and 12 hours respectively and
C can empty it in 6 hours. If all
the three are opened at 7 a.m.,
at what time will one-fourth of the
tank be filled ?
(1) 10 a.m. (2) 10 p.m.
(3) 11 p.m. (4) 11 a.m.
8
46The cost of 97 metre of cloth is Rs
242.50. What length of this can be purchased for Rs ( 302.50 ? )
8
47If ( x & y ) are in inverse proportion then
find proportionality constant at ( boldsymbol{x}= )
( mathbf{3}, boldsymbol{y}=mathbf{2} )
A . 4
B. 5
( c .6 )
D.
8
48( A, B ) and ( C ) can finish a job working alone in 72,24 and 36 days respectively In how many days they can finish the job if they worked together?
A . 12
B. 9
c. 15
D. 18
8
4964. Two natural numbers are in the
ratio 3 : 5 and their product is
2160. The smaller of the num-
bers is
(1) 36
(2) 24
(3) 18
(4) 12
8
50Rashmi has a road map with a scale of
1 cm representing 18 km. She drives on a road for ( 72 mathrm{km} ). What would be her
distance covered in the map?
8
51The line ( A D ) is divided in the ratio of
( A B: B C: C D=1: 3: 4 . ) If ( A B= )
( 0.8 mathrm{cm}, ) calculate the length of ( A D )
A . ( 3.5 mathrm{cm} )
B. ( 6.4 mathrm{cm} )
c. ( 5.89 mathrm{cm} )
D. ( 6.5 mathrm{cm} )
8
52Which of the following are in inverse
proportion?
(i) The number of workers on a job and
the time to complete the job.
(ii) The time taken for a journey and the distance travelled in a uniform speed.
(iii) Area of cultivated land and the crop
harvested.
(iv) The time taken for a fixed journey and the speed of the vehicle.
(v) The population of a country and the area of land per person.
8
5311 men can dig ( 6 frac{3}{4} ) metre long trench in one day. How many men should be employed for digging 27 metre long trench of the same type in one day?8
54cost of 10 mangoes is Rs. 100 The cost of
18 mangoes is
A . Rs. 18
B. Rs. 108
c. Rs. 200
D. Rs. 180
8
5553. Two numbers are in ratio
5 : 8. If their difference is 48,
then the smaller number is
(1) 80 (2) 96
(3) 128 (4) 64
8
564 men or 6 women earn Rs 360 in one
day. Find how much will 6 men and 4
women earn in one day?
A . Rs 780
B. Rs 720
c. Rs 760
D. Rs 740
8
57ff ( y ) varies inversely as ( x, ) and ( y=9 ) when ( x=2, ) find ( y ) when ( x=3 )8
58A farmer has enough food to feed 20
animals in his cattle for 6 days. How long would the food last if there were 10
more animals in his cattle?
8
59In a Television game show, the prize money of Rs 1,00,000 is to be divided equally amongst the winners. Complete the following table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners?
Number of winners
Prize for
each
[
begin{array}{rr}
50,000 \
, 00,000
end{array}
]
winner (in Rs.)
8
60Which of the following ( a & b ) are in direct proportion?
A ( cdot a=frac{2}{b} )
В. ( a=2 b )
c. ( a=b^{3} )
D. ( a=frac{1}{b^{2}} )
8
6151.
The cost of making an article is
divided between materials, la-
bour and overheads in the ratio
3:4:2. If the cost of material
33.60, the cost of article is
(1) 100.80 (2) 11.20
(3) 44.80 (4) 22.40
8
6218 men can reap a filed in 35 days. For
reaping the same filed in 15 days, how many men are required?
8
63A fort is provisioned for 42 days. After 10 days, a reinforcement of 200 men
arrives and the food will now last only 24
days. How many men were there in the fort?
A .200
в. 600
( c .500 )
D. 300
8
64f ( a, b, c, d ) are in continued proportion,
prove that ( (a+d) b+c)-(a+c)(b+d)= )
( (b-c)^{2} )
8
65The cost of 2 meter cloth is ( 10 . ) Find the
( operatorname{cost} ) of ( 100 m ) cloth.
A . 400
в. 500
( c .1000 )
D. 1500
8
66A work – force of 420 men with a
contractor can finish a certain piece of work in 9 months. How many extra men
must he employ to complete the job in 7 months?
8
67If ( boldsymbol{a}: boldsymbol{b}=mathbf{5}: mathbf{9} ) and ( boldsymbol{b}: boldsymbol{c}=boldsymbol{4}: mathbf{7} ) find ( boldsymbol{a}: )
( boldsymbol{b}: boldsymbol{c} )
This question has multiple correct options
A ( cdot 5: 9: frac{63}{4} )
B. 20: 63: 36
( mathbf{c} cdot 4: 36: 63 )
D. 20: 36: 63
8
68Eight oranges can be bought for Rs
10.40, then how many more oranges can be bought for Rs ( 16.90 ? )
A. 5 oranges
B. 3 oranges
c. 7 oranges
D. 2 oranges
8
6914 apples cost Rs. 140 The cost of 1 apple
is
A. Rs. 10
B. Rs. 8
c. Rs. 4
D. Rs. 14
8
70If 36 men can do a piece of work in 25 days, in how many days will 15 men do it
( ? )
8
71Which is example of inverse proportion?
A. Length of edge of square & its area
B. Speed and time taken
C. Length of edge of square ( & ) its perimeter
D. Quantity of pencils & total cost
8
72State true or false:
Following are the car parking charges near a railway station upto
4 hours Rs 60
8 hours Rs 100
12 hours Rs 140
24 hours Rs 180
Hence, the parking charges are in direct proportion to the parking time.
A. True
B. Fals
8
73Rohit bought 12 registers for Rs 156, find the cost of 7 such registers. (in Rs.)8
74If ( a ) is directly proportional to ( b ) and ( b ) is inversely proportional to ( c . ) Then
what is the proportionality between ( a )
and ( c ? )
A . Direct
B. Inverse
c. sometimes direct sometimes inverse
D. Can’t be determined
8
75Four pipes can fill a tank in 70 min. How Iong will it take to fill the tank by 7 pipes?
A . 20 min
B. 35 min
( c .40 ) min
D. None of these
8
76D
10

Aman can row at 8 kmph in still water. If the river is running
at 2 kmph, it takes him 48 minutes to row to a place and
back. How far is the place?

1
100
8
7735 workers can build a house in 16
days. How many days will 28 workers working at the same rate take to build
the same house?
A. 16 days
в. 28 days
c. 20 days
D. 10 days
8
78Find inverse proportionaly constant if ( x ) and ( y ) are in inverse proportion.
[
]
begin{tabular}{l}
6 \
hline
( mathbf{A} cdot mathbf{9} )
B. 18
c. 27
D. 30
8
79If light can travel 31 times around the world in 4 seconds, how many times can it circle the world in 10 seconds.
A. 124 times
в. ( 66 frac{1}{2} ) times
c. ( quad 82 frac{1}{2} ) times
D. 77.5 times
8
80( boldsymbol{m}: boldsymbol{n} )8
81On a scale of map, ( 0.6 mathrm{cm} ) represents 6.6km. If the distance between the
points on the map is ( 80.5 mathrm{cm}, ) the actualdistance between these points is
( mathbf{A} cdot 9 mathrm{km} )
в. ( 72.5 mathrm{km} )
c. ( 190.75 mathrm{km} )
D. ( 885.5 mathrm{km} )
8
82( begin{array}{ccccc}boldsymbol{x} & mathbf{2} & boldsymbol{4} & mathbf{2 0} & mathbf{1 5} \ y & 3 & 7 & 10 & 12 \ z & 10 & 5 & 1 & 4 / 3end{array} ) Observe the table and find the
quantities which are in inverse
proportion
A. ( x ) and ( y )
B. ( x ) and ( z )
( mathbf{c} cdot y ) and ( z )
D. None of the above
8
83Which is an example of direct
proportion?
A. More working hours, more earning
B. More speed of car, less time taken
C. More no. of workers, less time taken
D. Less the age of person, more active he is
8
8456. A does 20% less work than B. If
A can complete a piece of work
in 7
hours, then B can do it in
(1) 10 hours
(3) 6 hours
(2) 4 hours
(4) 8 hours
8
85Three spraying machines working together can finish painting a house in 60 minutes. How long will it take for 5 machines of the same capacity to do the same job ?(in minutes)8
86The cost of 5 tables and 6 chairs is
Rs. ( 2884 . ) What is the cost of 15 tables
and 18 chairs?
A. ( R s .3300 )
в. ( R s .7332 )
c. ( R s .5600 )
D. ( R s .8652 )
8
87In 15 days, the earth picks up ( 1.2 times 10^{8} )
kg of dust from the atmosphere. In how many days it will pick up ( 4.8 times 10^{8} mathrm{kg} )
of dust?
8
88Kamal can do a piece of work in
12 day. -hich Debashis can fin-
ish in 10 days. If they work at it
on alternate days with Debashis
beginning in how many days, the
work will be finished ?
(1) 10 days (2) 10 days
3 11 days (4 11 days
8
89Complete the following table if ( boldsymbol{x} propto boldsymbol{y} )
[
x
]
( begin{array}{lllll}1 & 2 & 3 & – & 5end{array} )
( 4 quad 8 ) 16 ( – ) ( y ) 1
8
90How many men must be engaged to do
a piece of work in 16 days which 24 men can do in 40 days?
8
91In library 136 copies of a certain book require a shelf-length of 3.4 metre. How many copies of the same book would occupy a shelf-length of 5.1 meters?8
9264. 36 workers can do a piece of
work in 55 days. 66 workers can
do twice of this work in
(1) 33 days (2) 40 days
(3) 60 days (4) 44 days
8
93In a hostel of 50 girls, there are food provisions for 40 days. If 30 more girls join the hostel, how long will these provisions last ? (in days)8
94If ( frac{a}{b}-frac{c}{d}=0 ) and ( b c=7, ) then determine
the true statement among the following.
A. a and b are directly proportional.
B. a and c are inversely proportional.
c. a and d are inversely proportional.
D. b and c are directly proportional.
E. c and d are inversely proportional.
8
95Mark the correct alternative of the
following.
Two numbers are in the ration 3: 5 and
their sum is ( 96 . ) The larger number is?
A . 36
B. 42
c. 60
D. 70
8

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