Chapter No 2:
Ratio and Proportion
What is ratio?
✓ A ratio is the comparison of two or more quantities of the same kinds.
✓ A ratio may be written as “a : b” or “a/b” or “a is to b” or “a to b”.
✓ Ratios are represented mathematically by separating each quantity with a colon(:) for example,
the ratio 2:3, which is read as the ratio "two to three".
✓ The quantities separated by colons are sometimes called terms.
✓ The quantities to be compared must be measured in same units.
✓ The order of ratio is important.
✓ A ratio has no units.
Topic No 1.
Express the following Ratio in the simplest form:
Conversion scale:
✓ 1 hour = 60 minutes,
✓ 1 m = 100 c.m,
✓ 1 minute = 60 seconds
✓ 1 feet = 12 inches
✓ 1 kg. = 1000 gm,
✓ 1 year = 365 days,
✓ Rs 1 = 100 paisa,
✓ 1 month = 30 days
✓ 1 dozen = 12 pieces
✓ 1 day = 24 hours,
Simplify the following ratios:
Q no 1.
10:20
Q no 2.
240:320
Q no 3.
15:35:45
Q no 4.
120:220:360
Q no 5.
480000:360000
Q no 6.
Rs 3 : Rs 9
Q no 7.
Rs 2 : 40 paisa
Q no 8.
RS 2 and 40 paisa : 60 paisa
Q no 9.
2 eggs : 2 dozen eggs
Q no 10.
4 bananas: 4 dozen bananas
Q no 11.
2 Kg : 25 gm
Q no 12.
2.5 Kg : 500 gm
Q no 13.
50 grams: 20 gm: 2 Kg
Q no 14.
4 weeks : 4 days
Q no 15.
4 months : 12 months
Q no 16.
2 months : 20 days
Q no 17.
3 feet: 4 inches
Q no 18.
1.3 : 3.9
Q no 19.
2.5 : 7.5
Q no 39.
*2:1,
*2:3
Q no 40.
*2:45
Q no 41.
*3:2
Q no 42.
*3:4
*1:4
Q no 43.
*2:1
Q no 44.
*1:3
*1:5
Q no 45.
*20:1
Q no 46.
*5:20
Q no 47.
3:85
Q no 48.
1:4
Q no 49.
*1:15
Q no 50.
*1:15
Q no 51.
*2:9
*9:2
Q no 20.
Q no 21.
Q no 22.
Q no 23.
Q no 24.
Q no 25.
Q no 26.
Q no 27.
Q no 28.
Q no 29.
Q no 30.
Q no 31.
Q no 32.
Q no 33.
Q no 34.
Q no 35.
Q no 36.
Q no 37.
Q no 38.
3 months : 2 years
4 m : 40 cm
5 cm : 2 m
3 m and 15 cm : 15 cm
1/3: 4/3:5/3
1/5:2/3:3/4
77 days : 2 weeks
250 gm : 45kg: 450 gm
3/2:1/4:3/8
12 hours : 36 hours
20% : 60%
2 hours : 20 minutes
396000:150000:75000
15% to 135%
4 min : 3 hours
2100 : 3500
9/81
5min : 30 sec
30 min to 3 hours & 30 sec.
5 Years MCQs
The ratio of 30 inches to 5 feet is
2018
*1:2
*3:60
The ratio of 2 hours to 45 minutes is:
2017, 2012P
*60:45
*8:3
*4:3
In a certain college, there are 360 boys and 240 girls. The ratio of boys to girls is:
*2:3
*5:3
*3:5
2014P
The ratio of 12 days to 8 weeks 2
*3:14
*None of these
2013R
The ratio of 5 feet to 30 inches is:
*1:2
*1:6
*6:1
2013P, 2007
The ratio of 30 Min to 1.5 hours
*1:7
*1:9
2012R
The ratio of 1 Kg to 50 gm
2011R
*1;20 *1:50 *51:1
The ratio of 50 gm to 2KG is
2008
*1:40 *50:2 *none
The ratio of 85 Paisa to Rs 3
2011P
17:60
60:17
85:3
The ratio of 50 Paisa to Rs 2:
2009
2:50
4:1
50:2
The ratio of 5 Rupees and 75 paisa is:
2006
*15:1 *3:20 *20:3
The ratio of 3 Rupees and 80 paisa is:
2003R
*15:4 *3:20 *20:3
The ratio of 40 minutes to 2 hours and 20 minutes is
2003P
*4:2
*none
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Topic No 2.
Continues Ratio
Example
If a:b = 3:4 and b:c 2:3 then find A:B:C
A:B:C
3 4
2 3
6 8 12
Then Divide by 2
6 3:8 4 :12 6
3:4:6 ans
Find the ratio i.e a:b:c when
Q no 52. a:b = 3:4 and b:c 2:3
Q no 53. a:b = 4:6 and b:c 3:7
Q no 54. a:b 12:4 and b:c 3:6
Q no 55. a:c = 5:3 and a:b = 7:2
Q no 56. a:c = 9:7 and a:b 3:5
Q no 57. a:c = 2:8 and a:b = 1:3
Q no 58. X:Y =4:5 and Y:Z = 2:3
Q no 59. X:Z = 5: 4 and X:Z = 3: 6
Q no 60.
Q no 61.
*3:7:5
Q no 62.
Q no 63.
Find the ratio
Q no 64.
Q no 65.
Q no 66.
Q no 67.
Q no 68.
2014R
If a:b = 13:4 and b:c = 5:6 find a:b:c
2017, 2013P
If A: B = 3:5 and B:C is 5: 7 then A:B:C is
*7:5:3
*3:5:7
*1:1:1
2011R
If A: B = 5:7 and B:C is 3: 14 then A:B:C is
2007
If A: B = 5:6 and B:C is 8: 15 then A:B:C is
a:b:c:d when
a:b = 2:7 and b:c 2:4 and b:d= 2:8
a:b = 1:5 and b:c 3:8 and b:d= 4:9
a:c = 4:8 and a:b = 1:5 and a:d 2:5
a:c = 3:5 and a:b = 1:5 and b:d 5:15
a:c = 2:4 and a:b = 3:6 and c:d 7:9
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Topic No 3.
Distribution through ratio
Example
Distribute Rs 9,000 between Adnan and Salman in the Ratio of 1:2
Solution
Adnan : Salman
1
: 2
Sum of Ratio = 1+ 2 = 3
Adnan’s Share = Total Amount x
Adnan’s Share = 9000 x
Ratio .
Sum of Ratio
1.
3
Adnan’s Share = Rs 3,000
Salman’s Share = 9000 x 2 .
3
Salman’s Share = Rs 6,000
2014R
Distribute an a amount of Rs 68,000 among three person in the ratio of 1:5:4.
2012R
Q no 70. Distribute an a amount of Rs 7800 among three person in the ratio of 1:5:4.
2011P
Q no 71. Distribute an a amount of Rs 50,000 among three person A,B & C in the ratio of 10:5:1.
2004
Q no 72.
A, B and C are business partners. They earn a profit of Rs 24,000. Find the shares of
each partners in the profit if the profit can be shared in the ratio 2:5:3.
2008
Q no 73. Divide Rs. 100, 000 between Noman and Atif such that Noman gets double of what Atif gets.
2018
Q no 74. Distribute profit of Rs 50,000 among three partners Jawad, Areeba and Hamza such that
jawwad and Areeba Get the profit in the ratio of 5:3 whereas Areeba and Hamza get 3:2
2017
Q no 75. Distribute Rs 93,000 among three friends A,B,C such that A and B Get the profit in the ratio of 1:3
whereas B and C get 4:5.
2014P
Q no 76. Distribute Rs 36000 profit among three businessmen A, B, C such that A:B= 3:2 and B:C = 4:5.
2013R
Q no 77. Three bankers A, B, C invest Rs 20,000 ; 25,000 and Rs 30,000 respectively. Find the share of
each partner if they got profit of Rs 6,000/=
2003R
Q no 78. A, B and C invested jointly a sum of Rs 40,000, Rs 50,000 and Rs 10,000 respectively in a
computer business. If the profit was Rs 35,000 at the end of year, Find the share of the profit of each
investor.
2003P
Q no 79. Three men took part in a business. They put in Rs 2,000, Rs 4000 and Rs 1500 as their capitals.
The profit was divided among them in the same ratio as the amount invested by them. If the profit was Rs
300 what did each get?
2002P
Q no 80. A, B and C invested jointly a sum of Rs 7,000, Rs 14,000 and Rs 9,000 respectively in a
business. If the profit was Rs 9900 at the end of year, Find the share of the profit of each investor.
2013P
Q no 81. Distribute an amount of Rs 2400 among three persons, A,B and C in the ratio of 1/10, 2/5, ½
2011R
Q no 82. Distribute an amount of Rs 1600 among three persons, A,B and C in the ratio of 1/10, 2/5, ½
2007,2002R
Q no 83. Distribute an amount of Rs 5100 among three persons, A,B and C in the ratio of 1/2, 2/3, ¼
Q no 69.
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What is proportion?
A proportion is a statement that two ratios are equal. Or equality of two ratios is called
proportion. a:b::c:d where a:d is called extreme and b:c is called means.
There are three types of proportion
1. Direct Proportion
When one variable increase and another is also increase or when one variable decreases and
other also decreases then it is called direct proportion. In this type of proportion, both variables
moves in same direction.
2. Indirect or inverse Proportion
When one variable increases but other decreases then its called Inverse proportion. In this type
of proportion, both variables moves in opposite direction.
3. Combined/ Compound proportion
In this type of proportion there are more than two variables and all variables are may be direct
and indirect proportion
Topic No 4.
Direct Proportion
Example
The Cost of 5 pen is Rs 60 then find the cost of 10 pen
Pen
5
10
Cost
60
𝑥
a : b :: c : d
5: 60 :: 10 : 𝑥
Formula
a.d = b.c
5 x 𝑥 = 60 x 10
5𝑥 = 600
𝑥 = 600/5
𝑥 = Rs 120
.
2010
The Cost of 10 chairs is Rs 3250. Find the cost of 7 chairs.
2002
Q no 85. 125 Kg of rice cost Rs 3500 Kg of rice can be bought for Rs 2380
2006
Q no 86. A typist can type 350 words in 7 minutes. Then the number of words typed in 5
minutes will be?
2005
Q no 87. At present the ages of khalid and sohail are in the ratio of 4:3. in 6 years times
khalid will be 26 years old. How old is sohail at present.
Q no 84.
Q no 88.
If 12 boxes of soap weight is 36 Kg. what will be weight of 6 boxes.
Q no 89.At present the ages of adnan and salman are in the ratio of 1:4. in 7 years adnan will be
47 years old. How old is salman (a) at present (b) in 7 years.
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Topic No 5.
Indirect Proportion OR Inverse proportion
Example
5 men paint a building in 6 days. How long would 10 men take.
Men
5
10
Days
6
𝑥
a : b :: c : d
5: 6 :: 10 : 𝑥
Formula
a.b = c.d
5 x 6 = 𝑥 x 10
30 = 10𝑥
30/10 = 𝑥
𝑥 = 3 days
2014R
20 men paint a building in 5 days. How long would 8 men take.
2012P
Q no 91. 19 men paint a building in 5 days. How long would 9 men take.
2011P
Q no 92. Nine men paint a building in 21 days. How long would 7 men take
2002P
Q no 93. In a garrison, there is provision for 30 days for 14 soldiers. After 5 days 4
soldiers left. For how many days will be the provision last.
Q no 90.
Q no 94. In a camp has enough food to last 30 days for his 60 soldiers. If 10 soldiers are
also joint this company. How long can the same foods last?
Q no 95. Ten persons can dig a water tank in 4 days. How long will 5 persons take to dig
the same tank?
Q no 96. A train reaches from Hyderabad to Karachi in 2 hours at a speed of 200 Km per
hour. If the train is late due to some technical problem and reached in 3 hours. What
would be the speed of the train?
Q no 97. A construction company estimates that he needs 50 workers to complete a work
in 25 days. If he asked to complete the work in 15 days. Find the additional number of
workers he has to employed?
Q no 98. 36 workers build a house in 20 days. How many days will 18 worker working at
the same rate take to build the same house
Q no 99. At a scouts camp there is sufficient food to last 72 days. If 18 scouts leave the
camp, how much longer can the food last.
Q no 100. If takes 3 taps to fill a swiming pool in 8 hours. How long would it take to fill 5
taps.
Q no 101. In a graze yard there is a feed for 40 cows for 20 days. How many cows have to
leave the graze yards so that the same feeds can be used for 30 days.
Q no 102. In a warehouse there was a food storage for 90 days for 400 peoples. After 20
days 50 people left, now how long would it take to finish the food.
Q no 103. A flyover is constructed by 84 workers in 300 days. If 15 more workers joined
them, now how long would it take to complete the flyover.
Q no 104. 4 men can plough a filed in 15 hours. How long would it take 6 men to do the
work.
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Topic No 6.
Compound Proportion
Example
5 Men build 20 rooms of equal size in 9 days. How long will 10 men takes to complete 40
rooms?
Men
5
10
5
10
=
Rooms
20
40
20
40
0.5 =
x
Days
9
𝑥
𝑥
9
20𝑥
360
0.5 x 360 = 20 𝑥
180
180
20
= 20 𝑥
= 𝑥
𝑥 = 9 𝑑𝑎𝑦𝑠
2018
Q no 105.
30 Men build 15 rooms of equal size in 18 days. How long will 20 men takes to
complete 10 rooms?
2016
Q no 106.
30 labors construct 15 rooms of equal size in 18 days. In How many days can 12
labor construct 12 rooms of the same size?
2004
Q no 107.
25 labors construct 15 rooms of equal size in 18 days. In How many days can 10
labor construct 10 rooms of the same size?
2017
Q no 108.
40 machines produce 1000 screws in 100 hours. How many screws can 24
machines produce in 60 hours.
2015
Q no 109.
195 Men working 10 hours a day can finish a job in 20 days. How many men
should be employed to finish the job in 15 days works 13 hours a day.
2013R
Q no 110.
If 15 men drink 60 gallons of water in 20 days, how many gallons will 25 men
drink in 5 days,
2012R, 2005
Q no 111.
if 9 men consume 120 kg of rice in 20 days. In how many days will 15 men
consume 250 kg of rice?
2012P, 2003R
Q no 112.
5 photocopiers can produce 90000 copies in 6 hours a day. How many
photocopiers will be required to produce 16800 copies working 8 hours a day?
2011R
Q no 113.
If 1400 men make 11 miles of railroad in 12 weeks, how long will it take 2400
men to make 27.5 miles of such road.
2006
Q no 114.
If 500 men make 11 miles of railroad in 13 weeks, how long will it take 2000 men
to make 27.5 miles of such road.
2010
Q no 115.
Eight machines can produce 560 units per day working 6 hours a day. How many
machines are required to produce 1680 units per day working 9 hours a day.
2009
Q no 116.
If 9 men are paid Rs 15,120 for 7 day’s work. What will be the wages of 8 men
for 5 days
2008, 2002R
Q no 117.
20 men can build a road 15 km long in 18 days how long will 25 men take to
complete a 10 km long road.
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AIMS
2007
Q no 118. A soap factory makes 600 units in 9 days with the help of 20 machines. How
many units can be made in 12 days with the help of 18 machines?
Topic No 7.
Find the value of x in each problem.
Example
If 𝑥 : 2 ::8 : 𝑥 then value of x is
By applying direct proportion
a : b ::c : d
𝑥: 2:: 8 : 𝑥
𝑥 x𝑥 =2x8
𝑥2 = 16
Taking square roots both side
√𝑥2 = √16
𝑥=±4
Q no 119.
Q no 120.
Q no 121.
Q no 122.
*16
Q no 123.
*20
Q no 124.
*2
Q no 125.
*36
Q no 126.
*4
Q no 127.
*±2
Q no 128.
Q no 129.
Q no 130.
*3
Q no 131.
Q no 132.
*±2
x : 15 :: 24 : 30
24 : 30 :: x : 26
X : 26 :: 24 : 30
The value of x in 4:3::x:12 is
*±6
*-6
*36
The value of x in x:4::10:2 is
*21
*22
*23
If x : 15 :: 24 : 30 then value of x is:
*10
*12
*16
If 4 : x :: x : 9 then value of x is
*-6
*6
*±6
3 : 4 :: 6 : x
*24
*8
*12
9:x::x:4
*±3
*±4
*±6
3 : 4 :: 6 : x
6 : 3 :: 4 : x
In 10:6::8:x the value of x is
*6
*4
*none of these
X : 4 :: 3 : 2
2 : x :: x : 18
*±18 *±6
*6
2012R
2012P
2011R
2018
2016
2015
2014P, 2010, 2007
2013R
2013P
2011P
2009
2008
2004
2003R
Topic No 8.
Find the equivalent ratio
2003P
Which ratios are equal
28:36;
72:27;
21:27;
16:21
Q no 133. 2: 3, 20: 25, 12:18, 4: 7.
Q no 134. 48:24, 36:39, 6: 3, 21: 28.
Q no 135. 21:35, 18:27, 48: 64: 39: 65
Q no 136. 4:16, 21:35, 9:15, ¼:1, 1:4, 3:5
Q no 137. 24:28, 7:6, 30:35, 1/7:1/6, 6:14, 18:21.
Q no 138. 16:21, ¾:1, 15:20, 12:16, 4:6, 3:4.
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2016
Q no 139. If x:y = 3:7 then find
𝟓𝐱−𝐲
𝟑𝐱+𝟐𝐲
If x : y = 3 : 7
then
𝐱
𝟑
=
𝐲
𝟕
𝐱=
𝟑𝐲
𝟕
Put in equation
𝟑𝐲
𝟓 𝟕 −𝐲
𝟑𝐲
𝟑 𝟕 + 𝟐𝐲
𝟏𝟓𝐲
𝟕 −𝐲
𝟗𝐲
𝟕 + 𝟐𝐲
𝟏𝟓𝐲 − 𝟕𝐲
𝟗𝐲 + 𝟏𝟒𝐲
𝟖𝐲
𝟐𝟑𝐲
𝟖
𝟐𝟑
Q no 140. Find the ratio in the following equation
6x2 -23xy +20y2 0
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Home Work
Q no 141. Divide Rs 10,000 in the ratio of 2:3.
Q no 142. dived Rs 12,000 in the ratio of 1:3
Q no 143. Distribute Rs 45500 in two parts of 1:4.
Q no 144. Divide 900 in the ratio of 1: 2: 3
Q no 145. Distribute Net Income of Rs 9000 in two partners fifty-50( equally).
Q no 146. Distribute net loss of Rs 10500 in three partners equally.
Q no 147. A profit of Rs 24000 is to be divided among A,B and C in the ratio of 1/3,1/4 and 2/5.
Q no 148. A profit of Rs 48 000 is to be divided among A, B and C in the ratio of 2/3,1/5 and
3/4.
Q no 149. Divide Rs 20000 in the ratio of 20%: 30% and 50%.
Q no 150. Divide Rs 75000 in the ratio of 10% to A , 60% to B and balance to C.
Q no 151.
A,B and C are partners having capital of RS 200000, 400000 and 600000
respectively. It they earned net profit of Rs 24000. find the share of each partner.
Q no 152.
Adnan , Hussain and Umer are partners having capital of RS 36000, 48000 and
42000 respectively. It they earned net income of Rs 21000. find the share of each partner.
Q no 153.
A,B and C are equal partners having capital of RS 100000, 300000 and 500000
respectively. It they earned net profit of Rs 9000. find the share of each partner.
Q no 154.
The ratio of A and B is 1:3 while the ratio of B and C is 2 : 4. divide 12500 among
them.The ratio of X and Y is 2:5 while the ratio of X and Z is 3 : 4. divide 2000 among X,Y,Z.
Q no 155.
Find total profit If the ratio of A:B is 2:3 and A gets Rs 300.
Q no 156.
Divide 40000 in such a way that shabir gets double of zaki.
Q no 157.
divide 600 in three parts so than 4 times the first, 3 times the second and times
the third are all mutually equal.
Q no 158. The Cost of 10 books is Rs 750. How many books can be purchased in Rs 15000.
Q no 159. A carpenter makes 10 tables in 4 days. In how many days will he take to make 30
such tables.
Q no 160. If Ali can read 30 pages of a book in 3 days, then by the same rate how many pages
will be read in 11 days.
Q no 161.
A lift can carry goods upto 1600 Kg. how many boxes can be loaded on it if each
box weight 40 Kg.
Q no 162.
A child can solve 100 problems in 40 minutes. How much time will he take to
solve 150 such problems?
Q no 163.
A man covers a distance of 150 km in 5 days. Find the number of days that he
will cover a distance of 450Km with same speed.
Q no 164.
A computer operator types 300 words in 5 minutes. How many words he can
types in 10 minutes?
Q no 165.
Aslam saves Rs 450 in 2 months. How much time he will take to save Rs 1800?
Q no 166.
¾ of a property value is Rs. 615000. Find the value of the half property.
Q no 167.
If 15 boxes of juices weight is 2.25 Kg. what will be the eight of 5 boxes.
Q no 168.
A 6 ft man has a 4 ft shadow, hen a tree casts a 22 ft shadow. How tall is the
tree?
Q no 169.
45 men can paint 24 apartments in 2 weeks and 4 days. How long will 90 men
take to complete the 10 apartment in 5 days?
Q no 170.
A person travels 120 kilometers in 5 days walking 10 hours a day. How many
kilometers will he walk in 15 days of 8 hours days.
Q no 171.
If 235 men consume 517 Kilogram of wheat in 5 1/2 months, how many men will
consume 182 Kilograms of wheat in 7 months?
Q no 172.
10 machines produce 5000000 screws in 200 hours. How many screws can 24
machines produce in 60 hours.
Q no 173.
25 laborers can construct 15 rooms in 18 days in how many days can 10 laborers
complete 10 rooms of the same size.
Q no 174.
If 8 men earn Rs 9600 in 5 days. How much will 9 men earn in 7 days.
Q no 175.
10 photocopiers can produce 30,000 copies in 2 days and 4 hours a day. How
many photocopiers will be required to produce 15000 copies working 4 days and 4 hours a day?
Q no 176.
A garments factory makes 8150 shirts in 30 days with the help of 10 machines.
How many shirts can be made in 15 days with the help of 8 machines?
Q no 177.
A biscuit factory makes 1000000 packets of biscuits in 2 months, 3 weeks and 5
days with the help of 10 machines. How many biscuits can be made in 6 months, 4 weeks and 3
days with the help of 20 machines?
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AIMS