Unit 3
Ratio and Proportion
PRACTICE QUESTIONS: UNIT 3
1. A piece of string 64 cm long is divided in three pieces in the ratio 1: 2: 5.
Calculate the length of the longest piece.
Ans 1:
length of string = 64 cm
Ratio of pieces = 1:2:5
Sum of ratios = 8
Length of longest piece = 5/8
64
= 40 cm
2. A sum of money was to be shared among three persons A, B and C in the
ratio 2: 3: 5. If C receives $120 more than B, find the sum of money.
Ans 2:
let sum of money = $X
Ratio of A, B and C respectively = 2:3:5
Sum of Ratio = 10
Share of B = 3/10
$X
Share of C = 5/10
$X
As by given condition
Share of C = Share of B
3X/100 = 5X/100
$120
$120
Multiplying by 100 both side
3X = 5X
5X
$1200
3X = $1200
X = $600
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Unit 3
Ratio and Proportion
3. A car travels 81 km on 4.5 litres of petrol. How far can it travel on 20
litres of petrol?
Ans 3:
A car can travel on 4.5 liter of petrol = 81 km
A car can travel on 1 liter of petrol = 81/4.5 km
A car can travel 20 liter of petrol = 81/4.5
20
= 360 km
4. If 10 men complete a job in 25 days, how long will it take five men to do
the same job?
Ans 4:
Let number of men = X
Let number of days = Y
As in work number of men has inverse relation with number of days
So, by definition
X=k/Y
k=XY
When X = 10 and Y = 25
k= 250
Now when X = 5 then Y =?
Y = k/X = 250/5
= 50
It would take 50 days to do same job by 5 men.
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Unit 3
Ratio and Proportion
5. Share $150 among John, Mary and Sarah so that each of the two girls
receives twice as much as John.
Ans 5:
Total amount = $150
Ratio among John, Sarah and Mary respectively = 1:2:2
Sum of ratio = 5
i.
Calculate the amount of money John received.
Ans: John receive = 1/5 $150 = $30
ii.
Express John’s share as a fraction of the total amount.
Ans: John’s share as a fraction of the total amount = 30/150 = 1/5
iii.
Express Mary’s share as a fraction of the amount received by John
and Sarah.
Ans: Mary’s share = 2/5
$150 = $60
Similarly Sarah’s share = $60
Mary’s share as a fraction of the amount received by John and
Sarah = 60 / (60 + 30)
= 60/90 = 2/3
6. A piece of wood is divided into the ratio 3: 4: 2. The length of the longest
piece is 72 cm. Calculate the length of the piece of wood. (Q7)
Ans:
Let length of wood = X cm
Ratio of pieces = 3:4:2
Sum of ratio = 9
Longest piece = 72 cm
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Unit 3
Ratio and Proportion
According ratio rule
Longest piece = 4/9
X
So,
4X/9 = 72 cm
4X = 9
72 cm
X = 648/4 = 162 cm
7. (Q6)The diagram below shows a map of a golf course drawn on a grid of
1 cm squares. The scale of the map is 1: 4000. Using the map of the golf
course find:
i.
The distance, to the nearest m, from South Gate to East Gate.
ii.
The distance, to the nearest m, from North Gate to South Gate.
iii.
The area on the ground represented by 1 cm 2 on the map.
iv.
The actual area of the golf course in square metres.
North Gate
East Gate
South Gate
Ans: i: nearest distance from south to east gate is 4 unit i.e 160m
ii: nearest distance from south gate to north gate is 7 unit = 280m
iii: area on the ground represented by 1cm² = 1600m²
iv: approx actual area of the golf course in square meters = 41600m²
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