Kerala Syllabus Class 7 Mathematics - Unit 6 Ratio - Questions and Answers | Teaching Manual 

Questions and Answers for Class 7 Mathematics - Unit 6 Ratio - Study Notes | Text Books Solution STD 7 - Maths: Unit 6 Ratio - Questions and Answers | ഗണിതം - അംശബന്ധം - ചോദ്യോത്തരങ്ങൾ 

ഏഴാം ക്ലാസ്സ്‌  Mathematics - Unit 6 Ratio എന്ന പാഠം ആസ്പദമാക്കി തയ്യാറാക്കിയ ചോദ്യോത്തരങ്ങള്‍. ഈ അധ്യായത്തിന്റെ Teachers Handbook, Teaching Manual എന്നിവ ഡൗൺലോഡ് ചെയ്യാനുള്ള ലിങ്ക് ചോദ്യോത്തരങ്ങളുടെ അവസാനം നൽകിയിട്ടുണ്ട്.

Kerala Syllabus STD 7 Maths: Unit 6 Ratio - Textbook Solutions

♦ Textbook Activities (Textbook Page No: 87)
(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
Answer: 8:10 = 4:5 (Both divided by 2)

(ii) Height 8 metres; width 12 metres 
Answer: 8:12 = 2:3 (Both divided by 4)

(iii) Height 20 centimetres, width 1 metre
Answer: Converting both measurements into centimetres gives 20:100 = 1:5 (Both divided by 20)

(iv) Height 40 centimetres; width 1 metre
Answer: 40:100 = 2:5 (Both divided by 20)

(v) Height 1.5 centimetres; width 2 centimetres
Answer: 1.5:2 = 3:4  (Both multiplied by 2)

(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?
Height (cm) Width (cm)Ratio
68
3
3:4
¾1

13:4
615
2
 2:5
1
2:5

12:5
Answer:
Height (cm) Width (cm)RatioExplanation
683:4Both are divided by 2
343:4Since the ratio is 3:4 the width will be 4cm
¾1 3:4Both ¾ and 1 multiplied by 4, 
¾ x 4 = 3, 1 x 4 = 4
¾13:44 times 1 gives 4 and 4 times ¾ gives 3
6152:5Both are divided by 3
25 2:5Since the ratio is 2:5, the width 5cm
12½2:5The ratio is 2 to 5. So height 1 will have a width 2½.
(half of 5 is 2½, half of 2 is 1)
⅖12:55 times is 1 is 5. 5 times is ⅖ is 2
♦ Textbook Activities (Textbook Page No: 89)
Calculate the ratio, using the smallest possible numbers, in each of the following problems:
(1) Amina has 105 rupees with her, and Mercy has 175 rupees. What is the ratio of the smaller amount to the larger?
Answer: 105: 175, we can divide both numbers by 35. 
So the ratio can be written 105:175 = 3.5

(2) 96 women and 144 men attended a meeting. Find the ratio of the number of women to the number of men.
Answer: 96:144,  we can divide both numbers by 48 to obtain 96:144 = 2:3

(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: 7.5:4.5 = 5:3 (Both are divided by 1.5)

(4) When a rope was used to measure the sides of a rectangle, the width was ¼ of the rope 1 and the height was ⅓ of the rope. What is the ratio of the height to the width? 
Answer: 
¼:⅓ multiplying both numbers by 12 gives
¼ x 12 = 3⅓ x 12 = 4
¼:⅓ = 3:4

(5) 3½ glasses of water would fill a large bottle, and 2½ glasses of water could fill a smaller bottle. What is the ratio of the capacities of the larger bottle to the smaller bottle?
Answer: 3½ : 2½ = 7:5 (Both multiplied by 2)

♦ Textbook Activities (Textbook Page No: 90 - 91)
(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:
The ratio of rice to black gram is 6:2, which is equal to 3:1. When 3 x 3 cups = 9 cups of rice is taken,
black gram should be 3 x 1 = 3 cups

(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:
Sand should be 5 times that of cement (1:5)
Therefore sand = 45 x 5 = 225 sacks
1:5 = 45:225
∴ 225 sacks of sand are needed. (1 time 45 is 45; 5 times 45 is 225)

(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:
Paint and turpentine are in the 12:8 = 3:2 (3 x 4 = 12; 2 x 4 = 8)
If the paint is 5 times 3 = 15 litres
Turpentine should be 5 times 2 = 10 litres
3:2 = 5:10 

(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:
Here, women and men are in the ratio 11:10
The number of women = 1793
Since 1793 ÷ 11 = 163
1793 is 163 times 11
The number of men = 163 x 10 = 1630
The total number of men and women = 1793 x 1630 = 3423
Which is 163 times of (10 + 11)
That is 163 x 21 = 3423

♦ Textbook Activities (Textbook Page No: 92)
(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 investments. How much did each get?
Answer:
Suhara investment = 40000 rupees
Sita's investment = 50000 rupees
Ratio of their investments = 4:5
So, the profit was 4 + 5 = 9 rupees
Suhara would get 4 rupees, and Sita would get 5 rupees
Here, the profit is 9000 rupees, which is 1000 times 9 rupees
So, Suhra will get 1000 times 4 rupees = 4000 rupees
And, Sita will get 1000 times 5 rupees = 5000 rupees

(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
Ratio of the number of days each worked = 6:7
So, the total number of days = 13
6500 is 500 times of 13 (6500 ÷ 3 = 500)
Then Ramesan will get 500 times of 6 = 500 x 6 = 3000 rupees
John will get 500 times of 7 = 500 x 7 = 3500 rupees
Let's think this way:
Remesan will get ⁶⁄₁₃ part of the total, and John will get ⁷⁄₁₃ part of the total.
Therefore, the amount Remesan got = 6500 x ⁶⁄₁₃ = 3000 rupees
amount John got = 6500 x ⁷⁄₁₃ = 3500 rupees

(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?
Answer:
The ratio in which the amount is divided among Ramu and Raju = 3:2
Amount Ramu got = 480 rupees
This is 160 times of 3 (480 ÷ 3 = 160)
Then Raju got 160 times of 2 = 160 x 2 = 320 rupees
This can also be done using reciprocals:
Here, the ratio is 3:2
The 480 rupees Ramu got is ⅗ part of the total amount.
Then the total amount is ⁵⁄₃ times of what Ramu got, 
       = 480 x ⁵⁄₃ = 800 rupees
Raju got ⅖ th part of this 800 rupees
     = 800 x ⅖ = 320 rupees

(ii) What was the sum that was divided?
Answer:
480 + 320 = 800 rupees
Let's do this using reciprocals:
Ramu got ⅗ part of 480 rupees
That is total amount is ⁵⁄₃ times of 480 rupees.
    480 x ⁵⁄₃ = 800 rupees

(4) Draw a line AB, 9 centimetres long. Mark a point P on it. The lengths of AP
and PB should be in the ratio 1:2. How far away from A should we mark P?
Calculate and mark it.
Answer:
AP:PB = 1:2
1 part + 2 parts = 3 parts
9 is 3 times 3.
3 times 1 = 1 x 3 = 3
3 times 2 = 2 x 3 = 6
So AP = 3cm and PB = 6cm. That P is 3cm away from A.
(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:
Total length of PQ = 15cm
PX:XQ = 2:3
2 parts + 3 parts = 5 parts
15 is 3 times 5
PX = 3 times 2 = 2 x 3 = 6cm
XQ = 3 times 3 = 3 x 3 = 9 cm
(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 = 30cm
Ratio of the sides = 1:2
Taking the width as 1 and the length as 2,
perimeter = 1 + 2 + 1 + 2 = 6
30 ÷ 6 = 5. That is, 30 is 5 times 6.
Width of rectangle = 1 x 5 = 5cm
Length of rectangle = 2 x 5 = 10cm
Draw the rectangle yourself.

i) Rectangle with ratio 2:3
Perimeter = 30cm
Ratio of the sides = 2:3
Taking the width as 2 and the length as 3,
perimeter = 2 + 3 + 2 + 3 = 10cm
30 is 3 times 10
Width of rectangle = 2 x 3 = 6cm
Length of rectangle = 3 x 3 = 9cm
Draw the rectangle yourself.

Rectangle with ratio 3:7
Perimeter = 30cm
Ratio of the sides = 3:7
Taking the width as 3 and the length as 7,
perimeter = 3 + 7 + 3 + 7 = 20 cm
30 ÷ 20 = 1.5
That is 30 is 1.5 times 20
Width of rectangle = 3 x 1.5 = 4.5cm
Length of rectangle = 7 x 1.5 = 10.5cm
Draw the rectangle yourself.

(ii) Area of a rectangle with a ratio 1:2 = 5 x 10 = 50 sq.cm
Area of a rectangle with a ratio 2:3 = 6 x 9 = 54 sq.cm
Area of a rectangle with a ratio 3:7 = 4.5 x 10.5 = 47.25 sq.cm
Rectangle with ratio 2:3 has the largest area.