Students often refer to Kerala State Syllabus SCERT Class 7 Maths Solutions and Class 7 Maths Chapter 6 Ratio Questions and Answers Notes Pdf to clear their doubts.
SCERT Class 7 Maths Chapter 6 Solutions Ratio
Class 7 Maths Chapter 6 Ratio Questions and Answers Kerala State Syllabus
Ratio Class 7 Questions and Answers Kerala Syllabus
Page 87
Question 1.
Write down the ratio of the height to width of each of the following rectangles using the smallest possible natural numbers.
(i) Height 8 centimetres, width 10 centimetres
(ii) Height 8 metres; width 12 metres
(iii) Height 20 centimetres, width 1 metre
(iv) Height 40 centimetres; width 1 metre
(v) Height 1;5 centimetres; width 2 centimetres
Answer:
(i) Height 8 centimetres, width 10 centimetres.
The ratio of the height to width = 8 : 10 = 4 : 5
(ii) Height 8 metres; width 12 metres.
The ratio of the height to width = 8 : 12 = 2 : 3
(iii) Height 20 centimetres, width 1 metre.
i.e, Height 20 centimetres, width 100 centimetres.
The ratio of the height to width = 20 : 100 = 1:5
(iv) Height 40 centimetres; width 1 metre.
i.e, Height 40 centimetres, width 100 centimetres.
The ratio of the height to width = 40 : 100 = 2:5
(v) Height 1.5 centimetres; width 2 centimetres.
The ratio of the height to width – 1.5 : 2 = 3 : 4
Question 2.
In the table below, the height, width and their ratio of some rectangles are given, but only two of each. Can you calculate the third and complete the table.
Answer:
Page 89
Question 1.
Amina has 105 rupees with her and Mercy has 175 rupees. What is the ratio of the smaller amount to the larger?
Answer:
Amount with Amina =105 rupees
Amount with Mercy = 175 rupees
The ratio of the smaller amount to the larger = 105 : 175
= 3:5
Question 2.
96 women and 144 men attended a meeting. Find the ratio of the number of women to the number of men.
Answer:
Number of women = 96
Number of men =144
The ratio of the number of women to the number of men = 96 : 144
= 2:3
Question 3.
Of two pencils, the shorter is 4.5 centimetres long and the longer 7.5 centimetres. What is the ratio of the length of the longer to the shorter?
Answer:
Length of the longer pencil = 7.5 centimetres
Length of the shorter pencil = 4.5 centimetres
The ratio pf the length of the longer to the shorter = 7.5 : 4.5
= 5:3
Question 4.
When a rope was used to measure the sides of a rectangle, the width was \(\frac{1}{4}\) of the rope and the height was \(\frac{1}{3}\) of the rope. What is the ratio of the height to the width?
Answer:
Width = \(\frac{1}{4}\) of the rope
Height = \(\frac{1}{3}\) of the rope
The ratio of the height to the width = \(\frac{1}{3}: \frac{1}{4}\)
\(\frac{1}{4}=\frac{1 \times 3}{4 \times 3}=\frac{3}{12}\)
\(\frac{1}{3}=\frac{1 \times 4}{3 \times 4}=\frac{4}{12}\)
∴ Ratio = \(\frac{4}{12}: \frac{3}{12}\) = 4 : 3
Question 3.
3\(\frac{1}{2}\) glasses of water would fill a large bottle and 2\(\frac{1}{2}\) glasses of water could fill a smaller bottle. What is the ratio of the capacities of the larger bottle to the smaller bottle?
Answer:
Capacity of the large bottle = 3\(\frac{1}{2}\) glasses of water
= \(\frac{7}{2}\) glasses of water.
The capacity of the small bottle = 2\(\frac{1}{2}\) glasses of water
= \(\frac{5}{2}\) glasses of water
The ratio of the capacities of the larger bottle to the smaller bottle = \(\frac{7}{2}: \frac{5}{2}\)
= 7:5
Page 90,91
Question 1.
To make dosa, we need to take 2 cups of black gram for every 6 cups of rice. For 9 cups of rice, how many cups of black gram shall be taken?
Answer:
2 cups of black gram for every 6 cups of rice.
Ratio of black gram to rice = 2:6 = 1: 3
For 9 cups of rice,
Black gram : 9 = 1: 3
\(\frac{\text { Black gram }}{9}=\frac{1}{3}\)
Black gram = \(\frac{1}{3}\) × 9 = 3 cups
So, 3 cups of black gram should be taken for 9 cups of rice.
Question 2.
To plaster the walls of a house, cement and sand are mixed in the ratio 1: 5.45 sacks of cement were bought. How many sacks of sand are needed?
Answer:
The ratio of cement to sand = 1: 5 ,
45 sacks of cement were bought,
45: sand = 1 :5
\(\frac{45}{\text { sand }}=\frac{1}{5}\)
sand = 45 × \(\frac{1}{5}\) = 225 sacks
So, 225 sacks of sand are needed for 45 sacks of cement.
Question 3.
12 litres of paint was mixed with 8 litres of turpentine while painting the house. How many litres of turpentine should be mixed with 15 litres of paint?
Answer:
12 litres of paint was mixed with 8 litres of turpentine.
∴ The ratio of”turpentine to paint = 8: 12 = 2: 3
For 15 litres of paint,
Turpentine: 15 = 2:3
\(\frac{\text { Turpentine }}{15}=\frac{2}{3}\)
Turpentine = \(\frac{2}{3}\) × 15 = 10 litres.
So, 10 litres of turpentine should be mixed with 15 litres of paint.
Question 4.
In a ward of a panchayat, the women and men are in the ratio 11 : 10. There are 1793 women in the ward. How many men are there in the ward? What is the total number of women and men?
Answer:
The ratio of women to men = 11: 10.
There are 1793 women in the ward.
\(\frac{1793}{\mathrm{men}}=\frac{11}{10}\)
∴ Men = 1793 × \(\frac{10}{11}\) = 1630
Total number of women and men = 1793 + 1630 = 3423
Page 92
Question 1.
Suhara and Sita started a business. Suhara invested 40000 rupees and Sita 50000 rupees. They made a profit of 9000 rupees. It was divided in the ratio of their
Answer:
Amount invested by Suhara = 40000 rupees
Amount invested by Sita = 50000 rupees
Total profit = 9000 rupees
Ratio of investment of Suhara to Sita = 40000: 50000 = 4: 5
So, Suhara got \(\frac{4}{9}\) of the total profit and Sita got \(\frac{5}{9}\) of the total profit.
∴ Profit earned by Suhara = 9000 × \(\frac{4}{9}\) = 4000 rupees
Profit earned by Sita = 9000 × \(\frac{5}{9}\) = 5000 rupees.
Question 2.
Ramesan and John took up a contract for a work. Ramesan worked the first 6 days and John 7 days. They got 6500 rupees. They divided it in the ratio of the number of days each worked. How much did each get?
Answer:
Number of days Ramesan worked = 6 days
Number of days John worked = 7 days
Total amount they got = 6500 rupees
The ratio of the number of days worked by Ramesan to John = 6:7
So, amount Ramesan get is \(\frac{6}{13}\) of the toatal amount and John get \(\frac{7}{13}\) of the total amount.
Amount Ramesan get = 6500 × \(\frac{6}{13}\) = 3000 rupees
Amount John get = 6500 × \(\frac{7}{13}\) = 3500 rupees
Question 3.
When Ramu and Raju divided a sum of money in the ratio 3 : 2, Ramu got 480 rupees.
(i) How much did Raju get?
(ii) What was the sum that was divided?
Answer:
(i) The ratio of amount got by Ramu to Raju = 3:2
480 : Raju = 3: 2
\(\frac{480}{\text { Raju }}=\frac{3}{2}\)
∴ Raju = 480 × \(\frac{2}{3}\) = 320 rupees.
So, the amount Raju get = 320 rupees.
(ii) Total amount = 480 + 320 = 800 rupees.
Question 4.
Draw a line AB, 9 centimetres long. Mark a point P on it. The lengths of AP and PB should J>e in the ratio 1:2. How far away from A should we mark P ? Calculate and mark it.
Answer:
Length of AB = 9 cm .
AP : PB = 1:2
So, the length of AP is \(\frac{1}{3}\) of AB and that of PB is \(\frac{2}{3}\) of AB.,
∴ AP = 9 × \(\frac{1}{3}\) = 3 cm
PB = 9 × \(\frac{2}{3}\) = 6 cm
So, we have to mark P at a distance of 3 cm from A
Question 5.
Draw a line 15 centimetres long. Mark a point on it that divides the line in the ratio 2 : 3. Calculate the length and mark the point.
Answer:
Let AB = 15 cm and P be the point thet divide AB in the ratio 2:3.
i.e., AP: PB = 2: 3
So, the length of AP is j of AB and that of PB is \(\frac{3}{5}\) of AB.
∴ AP = 15 × \(\frac{2}{5}\) = 6 cm
PB = 15 × \(\frac{3}{5}\) = 9 cm
Question 6.
Draw a rectangle of perimeter 30 centimetres and sides of length in the ratio 1:2.
(i) With the same perimeter draw two more rectangles with sides in the ratio 2 : 3 and 3 : 7.
(ii) Calculate the areas of the three rectangles. Which rectangle has the greatest area?
Answer:
Perimeter of the rectangle = 30 cm
2 (length + breadth) =30
Length+breadth =15
The ratio of sides =1:2
∴ Length = \(\frac{2}{3}\) × 15 = 10 cm
Breadth = \(\frac{1}{3}\) × 15 = 5 cm
(i) The ratio of sides = 2:3
∴ Length = \(\frac{3}{5}\) × 15 = 9 cm
Breadth = \(\frac{2}{5}\) × 15 = 6 cm
The ratio of sides = 3:7
∴ Length = \(\frac{7}{10}\) × 15 = 10.5 cm
Breadth = \(\frac{3}{10}\) × 15 = 4.5 cm
(ii) Area of first rectangle = 10 × 5 = 50 cm²
Area of second rectangle = 9 × 6 = 54 cm²
Area of third rectangle = 10.5 × 4.5 = 47.25cm²
So, second rectangle has the greatest area.
Intext Questions And Answers
Question 1.
The walls of Aji’s house needs painting. First, 25 litres of green paint and 20 litres of white paint were mixed. To get the same shade of green, how many litres of green should be mixed with 16 litres of white?
Ans:
The ratio of green to white = 25: 20 = 5: 4
That is, 5 litres of green for every 4 litres of white.
4 times 4 litres is 16 litres.
So, 4 times 5 litres, 20 litres of green should be mixed with 16 litres of white.
In terms of ratio,
Green: White = 5: 4
For 16 litres of white,
Green: 16 = 5 : 4
\(\frac{\text { Green }}{16}=\frac{5}{4}\)
∴ Green = \(\frac{5}{4}\) × 16 = 20 litres
Question 2.
The school needs a vegetable garden. A rectangular plot is to be roped off for this. The length of the rope is 32 metres. They decided to have width and length in the ratio 3:5. What should be the width and length?
Answer:
Length of the rope = 32 metres.
So, perimeter of rectangular garden = 32 metres
2 (length + width) = 32
Length + width = 16
The ratio of width to length = 3: 5
∴ Length = 16 × \(\frac{3}{8}\) = 6 metres
Breadth = 16 × \(\frac{5}{8}\) =10 metres
Class 7 Maths Chapter 6 Kerala Syllabus Ratio Questions and Answers
Question 1.
Angles of a linear pair are in the ratio 4: 5. What is the measure of each angle?
Answer:
Ratio of angles in the linear pair = 4: 5
Sum of angles = 180
In 180, \(\frac{4}{9}\) is one angle and – is the other angle.
So, one angle = 180 × \(\frac{4}{9}\) = 80°
Other angle = 180 × \(\frac{5}{9}\) = 100°
Question 2.
Sita and Soby divided some money in the ratio 1: 2 and sita got 400 rupees. What is the total amount they divided?
Answer:
Ratio in which money divided =1:2
Amount Sita got = 400 rupees
400: Sita =1: 2
\(\frac{400}{\text { Sita }}=\frac{1}{2}\)
∴ Sita = 400 × \(\frac{2}{1}\) = 800 rupees
So, total amount = 400 + 800 = 1200 rupees.
Question 3.
Ramesh’s father divided his saving as follows:
- \(\frac{2}{7}\) of his savings to Ramesh
- \(\frac{5}{7}\) of his savings to his mother.
Find the ratio of this division.
Answer:
Ratio = \(\frac{2}{7}: \frac{5}{7}\) = 2: 5
Question 4.
What does it mean to say that the width to length ratio of a rectangle is 1:1? What sort of rectangle is it?
Answer:
The width to length ratio of a rectangle is 1:1,
Which means, length = width
When the sides of a rectangle are equal, it will be a square.
Question 5.
Santha decided to give her salary to her children Ravi and Shinu in the ratio 3:2. If Ravi gets Rs.4500, then.
a) Find the amount Shinu gets?
b) How much salary does Santha get?
Answer:
(a) Ratio of amount got by Ravi to Shinu = 3:2
Amount Ravi got = 4500 rupees
4500: Shinu = 3:2
\(\frac{4500}{\text { Shinu }}=\frac{3}{2}\)
∴ Shinu = 4500 × \(\frac{2}{3}\) = 3000 rupees.
(b) Santha’s salary = 4500 + 3000 = 7500 rupees
Question 6.
Raju has an amount of 120 rupees and Mary has 180 rupees.
A) What is the ratio of the amounts Mary and Raju have?
(a) 3:2
(b) 2:3
(c) 6:5
(d) 5:9
B) Mother gave 60 rupees more to Mary. How much more money Raju needed to make the same ratio?
C) If they divide 800 rupees in the same ratio, how much amount did each get?
Answer:
A) Ratio of the amount Mary and Raju have = 180 : 120 = 3:2
B) Mother gave 60 rupees more to Mary.
Now the amount with Mary = 180 + 60 = 240 rupees.
240 : Raju = 3: 2
\(\frac{240}{\text { Raju }}=\frac{3}{2}\)
∴ Raju = 240 × \(\frac{2}{3}\) = 160
So, more money Raju needed = 160 – 120 = 40 rupees
C) Amount Raju got = 800 × \(\frac{2}{5}\) = 320 rupees
Amount Mary got = 800 × \(\frac{3}{5}\)
= 480 rupees.
Question 7.
Last year the ratio of the female teachers and male teachers of Ramapuram UP School was 6:1.
a) If the number of male teachers is 6, what is the number of female teachers? Instead of the female teachers who got transfer from the school, male teachers joined there. Now the ratio of the female teachers and male teachers is 11:10.
b) How many female teachers got transfer this year?
c) This year some female teachers and male teachers will be 1:1. If so, how many female teachers will retire this year?
Answer:
a) Ratio of female teachers to male teachers = 6:1
Number of male teachers = 6
Number of female teachers = 6 × 6 = 36
b) Total number of teachers = 36 + 6 = 42
Ratio = 11: 10
Number of female teachers = 42 × \(\frac{11}{21}\) = 22
So, number of female teachers transferred = 36 – 22 = 14
c) Number of male teachers = 42 × \(\frac{10}{21}\) = 20
So, inorder to become ratio 1:1, number of male teachers = number of female teachers
∴ The number of female teachers retire this year = 22 – 20 = 2
Practice Questions
Question 1.
Express the width and length in ratios.
(i) Width = 3 cm Length= 9 cm
(ii) Width = 6 cm Length= 14 cm
Answer:
(i) 1:3
(ii) 3:7
Question 2.
The perimeter of a rectangular garden is 28 metres. The ratio of length and width is given by 3:4. Find its length and width.
Answer:
6 cm, 8 cm
Question 3.
The capacity of small tank is 500 litres and big tank is 1500 litres.
(a) Find the ratio of the capacities of the small tank and the big tank.
(b) Small tank is fully filles with water and big tank is half filled. Then, find the ratio of the capacities of the small tank and the big tank.
(c) 1500 litres of water is distributed to the houses of Appu and Muthu in the ratio 3:2. How much water will each house get?
Answer:
(a) 1:3
(b) 2:3
(c) 900 litres, 600 litres
Question 4.
24 litres of curd was mixed with 96 litres of water to make buttermilk.
(a) What is the ratio of water and curd used?
(b) How many litres of water is needed to mix with 96 litres of curd to make buttermilk in the same ratio?
(c) How many litres of curd is needed to make 600 litres of buttermilk?
Answer:
(a) 4:1
(b) 384 litres
(c) 120 litres
Question 5.
Anu and Manu divided ah amount in the ratio 3:2. If Anu got 100 rupees more, what is the total amount they divide?
Answer:
500 rupees
Question 6.
(a) What part of the circle is shaded in the picture?
(b) What part of the circle is unshaded?
(c) What is the ratio of shaded to unshaded?
Answer:
(a) \(\frac{1}{4}\)
(b) \(\frac{3}{4}\)
(c) 1:3
Question 7.
For making idlis, rice and Urad are to be taken in the ratio 2:1. In 9 cups of such a mxiture of rice and urad, how may cup of rice and urad are taken?
Answer:
6 cups,3 cups
Question 8.
In a co-operative society, there are 600 members are male and 400 are female. An executive committee of 30 members is to be formed with the same male to female ratio as in the society. How many male and female members are to be there in the committee?
Answer:
8, 12
Question 9.
A rectangular piece of land is to be marked on the school ground for a vegetable garden.
Hari and Mary started making rectangle with a 24 metre long rope. Vimala teacher said it would be nice, if the sides are in the ratio 3:5. What should be length and width of the rectangle? .
Answer:
7.5 m , 4.5 m
Question 10.
When measuring the length of two buses with one rope the length of the first bus is \(\frac{2}{3}\) of the length of the rope and the length of the second bus was \(\frac{3}{5}\) of the length of the rope. What is the ratio between the length of the buses.
Answer:
10:9
Class 7 Maths Chapter 6 Notes Kerala Syllabus Ratio
When quantities like length are measured using a definite unit, we may not always get counting numbers; and it is this fact which led to the idea of fractions. In comparing the sizes of two quantities, one question is whether both can be given as counting numbers, using a suitably small unit of measurement. It is this question that leads to the idea of ratio. We can use ratio to compare parts of a whole also
- Generally, when we state ratios, we avoid fractions and decimals. In other words, the smallest possible counting number is used to express ratios. By multiplying or dividing the ratio by the same number, we can make it in terms of the smallest possible counting number.
- We can use ratios to express any two measures, not just lengths, as multiples and parts.
- In any mixture, components are in fixed ratio. So, by knowing the ratio one can find the quantity of one component if other is given.
- If we are given the ratio in which a quantity is divided, we can find how much each part is using this ratio.
Rectangle Problems
Consider the following rectangle.
In both the rectangles, the width is 3 times the height. Or we can say that the height is ^ times the width.
So, the ratio of width to height is 3 : 1 and the ratio of height to width is 1 : 3 (The ratio of width to height = 6 : 2 = 3 : 1 or 4.5 : 1.5 = 3 : 1)
If we extend the height and width by the same multiple or shorten them by the same fraction, the ratio remains the same.
Other Measures
We can use ratios to express any two measures (not just lengths) as multiples and parts. For example, .
Suppose we have a 15 litre bucket and a 25 litre bucket.
The small bucket holds \(\frac{15}{25}=\frac{3}{5}\) of what large bucket holds.
Or
we can say that,
The ratio of capacity of small bucket to large bucket = 15 : 25 = 3:5
- If we extend the height and width by the same multiple or shorten them by the same fraction, the ratio remains the same.
- We can use ratios to express any two measures as multiples and parts.
- In a mixture, the components are mixed in fixed ratio.
- We can use ratio to compare parts of a whole also.