## NCERT Solutions for Class 6 Maths Chapter - 12: Ratio and Proportion## Exercise 12.1
Number of boys = 15 Ratio of number of girls to the number of boys = Number of girls/Number of boys = 20/15 = 4/3 (5 is the common factor of both the numbers 20 and 15) Ratio of number of girls to the number of boys = 4: 3
Number of boys = 15 Total number of students = Number of girls + Number of boys = 15 + 20 = 35 Ratio of number of girls to the total number of students = Number of girls/Total number of students = 20/35 = 4/7 (5 is the common factor of both the numbers 20 and 35) Ratio of number of girls to the number of students = 4: 7
Students liking football = 6 Students liking cricket = 12 Remaining students = Total students - (student liking football + cricket) = 30 - (6 + 12) = 30 - 18 = 12 Thus, students liking tennis = 12
Students liking football = 6 Students liking tennis = 12 Ratio of the students liking football to the students liking tennis = Number of students like football/ Number of students liking tennis = 6/12 = 1/2 (6 is the common factor of both the numbers 6 and 12) Thus, Ratio of the students liking football to the students liking tennis = 1: 2
Students liking cricket = 12 Ratio of the students liking cricket to the total students = Number of students liking cricket / Total number of students = 12/30 = 2/5 (6 is the common factor of both the numbers 12 and 30) Thus, Ratio of the students liking cricket to the total students = 2: 5
Number of triangles = 3 Number of circles = 2 Number of squares = 2 Ratio of the number of triangles to the number of circles = Number of triangles/Number of circles = 3/2 Thus, Ratio = 3: 2
Number of triangles = 3 Number of circles = 2 Number of squares = 2 Ratio of the number of squares to the number of figures inside the rectangle = Number of squares /Number of figures = 2/7 Thus, Ratio = 2: 7
Number of triangles = 3 Number of circles = 2 Number of squares = 2 Ratio of the number of circles to the number of figures inside the rectangle = Number of circles /Number of figures = 2/7 Thus, Ratio = 2: 7
Speed = Distance/Time Speed = 9/Time Distance travelled by Akhtar = 12km Speed = Distance/Time Speed = 12/Time Ratio of speed of Hamid to the speed of Akhtar = Speed of Hamir/Speed of Akhtar = (9/Time)/ (12/Time) Since, the time are the same, it will cancel out. Ratio = 9/12 Ratio = 3/4 (3 is the common factor of both the numbers 9 and 12) Ratio = 3: 4
Here, we will consider two ratios at a time to find the missing value.
Let's compare the denominator of both the ratios. Dividing 18 by 6, we get: 18/6 = 3 It means that the numerator of the given ratio can also be divided by 3. 15/3 = 5 (3 × 5)/ (3 × 6) Thus, the missing number is 5.
Here, we need to find the denominator. So, we will compare the numerators of the next two ratios. 5 × 2 = 10 Similarly, multiplying 2 by 6, we get: 6 × 2 = 12 Thus, the denominator of the other missing ratio is 12.
Let's compare the denominator of both the ratios. 30/12 = 2.5 Or 12 × 2.5 = 30 Multiplying the numerator by 2.5, we get: 10 × 2.5 = 25 The numerator of the third missing ratio is 25. Thus, the given question with all the missing numbers can be written as: Whenever two ratios are specified in an equivalent equation, they are always tends to be equal. Hence, all the four ratios specified in the given question are
So, we will divide the ratio by its common factors, i.e., the common factors of both the numerator and the denominator.
Factors of 108: 3 × 3 × 3 × 4 81/108 can be written as: 81/108 = 3 × 3 × 3 × 3/ 3 × 3 × 3 × 4 Cancelling the common numbers, we get: 81/108 = 3/4 Thus, the ratio of 81 to 108 is 3: 4.
Factors of 63: 3 × 3 × 7 98/63 can be written as: 98/63 = (2 × 7 × 7)/ (3 × 3 × 7) Cancelling the common numbers, we get: = 14/9 Ratio = 14: 9
Factors of 121: 11 × 11 33/121 can be written as: 33/121 = (3 × 11) / (11 × 11) Cancelling the common numbers, we get: 33/121 = 3/11 Ratio = 3: 11
Factors of 45: 3 × 3 × 5 30/45 can be written as: 30/45 = (2 × 3 × 5) / (3 × 3 × 5) Cancelling the common numbers, we get: 30/45 = 2/3 Thus, Ratio = 2: 3
1 hour = 60 minutes 1.5 hours = 1.5 × 60 = 90 minutes Factors of 30: 3 × 2 × 5 Factors of 90: 3 × 3 × 2 × 5 30/90 can be expressed as: 30/90 = (3 × 2 × 5)/ (3 × 3 × 2 × 5) Cancelling the common numbers, we get: 30/90 = 1/3 Thus, Ratio of 30 minutes to 1.5 hours= 1: 3
1 m = 100 cm 1.5 m = 1.5 × 100 = 150 cm Factors of 40: 2 × 2 × 2 × 5 Factors of 150: 2 × 3 × 5 × 5 40/150 can be expressed as: 40/150 = (2 × 2 × 2 × 5)/ (2 × 3 × 5 × 5) Cancelling the common numbers, we get: 40/150 = 4/15 Thus, Ratio of 40 cm to 1.5 m= 4: 15
1 rupee = 100 paisa Factors of 55: 11 × 5 Factors of 100: 2 × 2 × 5 × 5 55/100 can be expressed as: 55/100 = (11 × 5) / (2 × 2 × 5 × 5) Cancelling the common numbers, we get: 55/100 = 11/20 Ratio = 11: 20 Ratio of 55 paise to ₹ 1 = 11: 20
1 litre = 1000 ml 2 litres = 2 × 1000 = 2000 ml Factor of 2000: 4 × 500 500/2000 can be written as: 500/2000 = (500)/ (4 × 500) Cancelling the common numbers, we get: = 1/4 Ratio = 1:4 Thus, ratio of 500 mL to 2 litres is 1: 4.
Money saved by Seema = 50,000 Ratio of money earned to the money saved = Earned money/ Saved money = 150000/ 50000 = (3 × 50000) /50000 = 3/1 Thus, the ratio of money earned to the money saved is
Money saved by Seema = 50,000 Money spends by Seema = Money earned - Money saved = 150000 - 50000 = 1, 0 0, 000 Ratio of money saved to the money spend = Saved money/ Spent money = 50000/ 100000 = (50000) / (2 × 50000) = 1/2 Thus, the ratios of money saved to the money spend
Total number of students in a school = 3300 Ratio of the number of teachers to the number of students = Number of teachers/ Number of students = 102/3300 Factors of 102: 2× 3 × 17 Factors of 3300: 3 × 11 × 2 × 50 102/3300 = (2× 3 × 17) / (3 × 11 × 2 × 50) 102/3300 = 17/550 Ratio of the number of teachers to the number of students =
Number of girls = 2300 Number of boys = Total students - Number of girls = 4320 - 2300 = 2020 Ratio of the number of girls to the total number of students = Number of girls/ Total students = 2300/4320 Factors of 2300: 23 × 2 × 2 × 5 × 5 Factors of 4320: 2 × 2 × 2 × 2 × 2 × 5 × 3 × 3 × 3 2300/4320 = (23 × 2 × 2 × 5 × 5) / (2 × 2 × 2 × 2 × 2 × 5 × 3 × 3 × 3) Cancelling out the common factors, we get: 2300/4320 = (23 × 5)/ (2 × 2 × 2 × 3 × 3 × 3) 2300/4320 = 115/216 Thus, Ratio of the number of girls to the total number of students =
Number of girls = 2300 Number of boys = Total students - Number of girls = 4320 - 2300 = 2020 Ratio of the number of boys to the number of girls = Number of boys/ Number of girls = 2020/2300 Factors of 2300: 23 × 2 × 2 × 5 × 5 Factors of 2020: 2 × 2 × 5 × 101 2020/2300 = (2 × 2 × 5 × 101) / (23 × 2 × 2 × 5 × 5) Cancelling out the common factors, we get: 2300/4320 = (101)/ (23 × 5) 2300/4320 = 101/115 Thus, Ratio of the number of boys to the number of girls =
Number of girls = 2300 Number of boys = Total students - Number of girls = 4320 - 2300 = 2020 Ratio of the number of boys to the total number of students = Number of boys/ Number of students = 2020/4320 Factors of 2020: 2 × 2 × 5 × 101 Factors of 4320: 2 × 2 × 2 × 2 × 2 × 5 × 3 × 3 × 3 2020/4320 = (2 × 2 × 5 × 101/ (2 × 2 × 2 × 2 × 2 × 5 × 3 × 3 × 3) Cancelling out the common factors, we get: 2020/4320 = (101)/ (2 × 2 × 2 × 3 × 3 × 3) 2020/4320 = 101/216 Thus, Ratio of the number of boys to the total number of students =
Total number of students = 1800 Number of students opting basketball = 750 Number of students opting cricket = 800 Number of students opting basketball tennis = Total students - (Number of students opting basketball + Number of students opting cricket) = 1800 - (750 + 800) = 1800 - 1550 = 250 Number of students opting basketball tennis = 250
Number of students opting basketball = 750 Number of students opting cricket = 800 Number of students opting basketball tennis = 250 Ratio of number of students who opted basketball to the number of students who opted table tennis = Students opting basketball/ Students opting tennis = 750/250 Factors of 750: 3 × 250 750/250 = (3 × 250)/ 250 = 3/1 Thus, Ratio = 3: 1
Number of students opting basketball = 750 Number of students opting cricket = 800 Number of students opting basketball tennis = 250 Ratio of number of students who opted cricket to the number of students who opted table basketball = Students opting cricket / Students opting basketball = 800/750 Factors of 750: 3 × 2 × 5 × 5 × 5 Factors of 800: 2 × 2 × 2 × 2 × 2 × 5 × 5 800/750 can be written as 800/750 = (2 × 2 × 2 × 2 × 2 × 5 × 5)/ (3 × 2 × 5 × 5 × 5) Cancelling out the common terms, we get: 800/750 = (2 × 2 × 2 × 2)/ (3 × 5) 800/750 = 16/15 Thus, Ratio = 16: 15 750/250 = (3 × 250)/ 250 = 3/1 Thus, Ratio = 3: 1
Number of students opting basketball = 750 Number of students opting cricket = 800 Number of students opting basketball tennis = 250 Ratio of number of students who opted basketball to the number of students = Students opting basketball/ Total students = 750/1800 Factors of 750: 3 × 2 × 5 × 5 × 5 Factors of 1800: 3 × 3 × 2 × 2 × 2 × 5 × 5 750/1800 can be written as: 750/1800 = (3 × 2 × 5 × 5 × 5) / (3 × 3 × 2 × 2 × 2 × 5 × 5) Cancelling out the common terms, we get: 750/1800 = 5/ (3 × 2 × 2) 750/1800 = 5 / 12 Thus, Ratio = 5: 12
Cost of a dozen pens = ₹ 180 Cost of 1 pen = 180/12 = 15 Cost of 1 pen = ₹ 15 Cost of 8 ball pens = ₹ 56 Cost of 1 ball pen = 56/8 = 7 Cost of 1 ball pen = ₹ 7 Ratio of the cost of a pen to the cost of a ball pen = Cost of 1 pen/Cost of 1 ball pen = 15/7 Thus, Ratio =
Here, we will consider two ratios at a time to find the missing value.
To find the numerator, we will find the relation between their denominators. 25 × 2 = 50 Similarly, 10 × 2 = 20 Thus, the numerator of the second ratio is 20.
To find the denominator, we will find the relation between their numerators. 20 × 2 = 40 Similarly, 50 × 2 = 100 The numerator of the third ratio is 100. Thus, The given ratios with their missing value can be represented as:
So, ratio of pens can be represented as: Ratio/ (Sum of ratio) × Total pens Share of Sheela = 3/ (3 + 2) × 20 = 3/5 × 20 = Share of Sangeeta = 2/ (3 + 2) × 20 = 2/5 × 20 =
Ratio = Age of Shreya/ Age of Bhoomika Ratio = 15/12 Ratio = (3 × 5)/ (3 × 4) = 5/4 Ratio = 5: 4 So, ratio of money can be represented as: Ratio/ (Sum of ratio) × Total money Share of Shreya = 5/ (5 + 4) × 36 = 5/9 × 36 = 20 Thus, the share of Shreya is rupees Share of Bhoomika = 4/ (5 + 4) × 36 = 4/9 × 36 = 16 Thus, the share of Bhoomika is rupees
Present age of father = 42 years Present age of son = 14 years Ratio = 42/14 = (2 × 3 × 7) / (2 × 7) = 3/1 Ratio = 3: 1 Thus, the ratio of the present age of father to the present age of son is 3: 1.
It means 2 years younger than the present age. Age of father = present age - 2 Age of father = 42 - 2 = 40 years Ratio = 40/12 = (2 × 2 × 2 × 5) / (2 × 3 × 2) Cancelling out the common factors, we get: Ratio = 10/3 Ratio = 10: 3
Present age of son = 14 years Age of father after 10 years = 42 + 10 = 52 years Age of son after 10 years = 14 + 10 = 24 years Ratio = Age of father after 10 years/ Age of son after 10 years = 52/24 = (2 × 2 × 13)/ (2 × 2 × 2 × 3) Cancelling out the common factors, we get: = 13/6 Ratio =
Present age of son = 14 years Age of father = 30 years It means 12 years younger than the present age. Age of son = Present age - 12 = 14 - 12 = 2 years Ratio = 30/2 = 15/1 Ratio = 15: 1 Thus, the ratio of the age of the father to the age of son is ## Exercise 12.2
We can write the above two ratios as: 15: 45:: 40: 120 '::' symbol divides the two ratios. We can also use an equal (=) sign to compare the two ratios. We need to convert the ratios to their lowest form. It makes the comparison easier.
15/45 15/(15 × 3) Cancelling out the common factors, we get: 15/45 = 1/3 So, Ratio = 1:3
40/120 = 40/ (40 × 3) Cancelling out the common factors, we get: 40/120 = 1/3 So, Ratio = 1:3 15:45 = 40:120
Both the ratios are equal. Hence, we can say that the given numbers are in proportion.
We can write the above two ratios as: 33: 121:: 9: 96 '::' symbol divides the two ratios. We can also use an equal (=) sign to compare the two ratios. We need to convert the ratios to their lowest form. It makes the comparison easier.
33/121 (11 × 3)/(11 × 11) Cancelling out the common factors, we get: 33/121 = 3/11 So, Ratio = 3: 11
9/96 = (3 × 3)/ (3 × 32) Cancelling out the common factors, we get: 9/96 = 3/32 So, Ratio = 3:32 3: 11 is not equal to 3: 32 33: 121 is not equal to 9: 96. Hence, we can say that the given numbers are not in proportion.
We can write the above two ratios as: 24: 28:: 36: 48 '::' symbol divides the two ratios. We can also use an equal (=) sign to compare the two ratios. We need to convert the ratios to their lowest form. It makes the comparison easier.
24/28 (4 × 6)/(4 × 7) Cancelling out the common factors, we get: 24/28 = 6/7 So, Ratio = 6: 7
36/48 = (12 × 3)/ (12 × 4) Cancelling out the common factors, we get: 36/48 = 3/4 So, Ratio = 3:4 6: 7 is not equal to 3: 4 24: 28 is not equal to 36: 48 Hence, we can say that the given numbers are not in proportion.
We can write the above two ratios as: 32: 48:: 70: 210 '::' symbol divides the two ratios. We can also use an equal (=) sign to compare the two ratios. We need to convert the ratios to their lowest form. It makes the comparison easier.
32/48 (16 × 2)/(16 × 3) Cancelling out the common factors, we get: 32/48 = 2/3 So, Ratio = 2: 3
70/210 = (70 × 1)/ (70 × 3) Cancelling out the common factors, we get: 70/120 = 1/3 So, Ratio = 1: 3 2: 3 is not equal to 1: 3 32: 48 is not equal to 70: 120 Hence, we can say that the given numbers are not in proportion.
We can write the above two ratios as: 4: 6:: 8: 12 '::' symbol divides the two ratios. We can also use an equal (=) sign to compare the two ratios. We need to convert the ratios to their lowest form. It makes the comparison easier.
4/6 (2 × 2)/(2 × 3) Cancelling out the common factors, we get: 4/6 = 2/3 So, Ratio = 2: 3
8/12 = (4 × 2)/ (4 × 3) Cancelling out the common factors, we get: 8/12 = 2/3 So, Ratio = 2: 3 2: 3 = 2: 3
Hence, we can say that the given numbers are in proportion.
We can write the above two ratios as: 33: 44:: 75: 100 '::' symbol divides the two ratios. We can also use an equal (=) sign to compare the two ratios. We need to convert the ratios to their lowest form. It makes the comparison easier.
33/44 (11 × 3)/(11 × 4) Cancelling out the common factors, we get: 33/44 = 3/4 So, Ratio = 3: 4
75/100 = (25 × 3)/ (25 × 4) Cancelling out the common factors, we get: 75/100 = 3/4 So, Ratio = 3: 4 3: 4 = 3: 4
Hence, we can say that the given numbers are in proportion.
We need to check that the given numbers are in proportion or not. For the comparison, the two ratios are converted to their lowest form. 16: 24 can be written as: 16/24 = (8 × 2)/ (8 × 3) Cancelling out the common factors, we get: = 2/3 Ratio = 2: 3 20:30 can be written as: 20/30 = (10 × 2)/ (10 × 3) Cancelling out the common factors, we get: = 2/3 Ratio = 2: 3 The given ratios are equal. Hence, the given two ratios are in proportion.
We need to check that the given numbers are in proportion or not. For the comparison, the two ratios are converted to their lowest form.
21/6 = (3 × 7)/ (3 × 2) Cancelling out the common factors, we get: = 7/2 Ratio = 7: 2
35/10 = (5 × 7)/ (5 × 2) Cancelling out the common factors, we get: = 7/2 Ratio = 7: 2 The given ratios are equal. Hence, the given two ratios are in proportion.
We need to check that the given numbers are in proportion or not. For the comparison, the two ratios are converted to their lowest form.
12/18 = (6 × 2)/ (6 × 3) Cancelling out the common factors, we get: = 2/3 Ratio = 2: 3
28/12 = (4 × 7)/ (4 × 3) Cancelling out the common factors, we get: = 7/3 Ratio = 7: 3 The ratios are not equal. Hence, the given two ratios are not in proportion.
8/9 It is already present in its lowest form, i.e., both the numerator and the denominator have the common factor 1.
24/27 = (3 × 8)/ (3 × 9) Cancelling out the common factors, we get: = 8/9 Ratio = 8: 9 The given ratios are equal. Hence, the given two ratios are in proportion.
5.2/3.9 = (1.3 × 4)/ (1.3 × 3) Cancelling out the common factors, we get: = 4/3 Ratio = 4: 3
The ratios are not equal. Hence, the given two ratios are not in proportion.
0.9/0.36 = (0.09 × 10)/ (0.09 × 4) Cancelling out the common factors, we get: = 10/4 Ratio = 10: 4 = 10: 4 The given ratios are equal. Hence, the given two ratios are in proportion.
The units in the ratio does not matter while comparison. The above statement can be represented as: 40: 200 = 15: 75
40/200 = (40 × 1)/ (40 × 5) = 1/5 Ratio = 1: 5
15/75 = (15 × 1)/ (15 × 5) Cancelling out the common factors, we get: = 1/5 Ratio = 1: 5 The given ratios are equal. Hence, the given two ratios are in proportion. The answer is
The units in the ratio does not matter while comparison. So, we will ignore the units. The above statement can be represented as: 7.5: 15 = 5: 10
7.5/ 15 = (7.5 × 1)/ (7.5 × 2) = 1/2 Ratio = 1: 2
5/10 = (5 × 1)/ (5 × 2) Cancelling out the common factors, we get: = 1/2 Ratio = 1: 5 The given ratios are equal. Hence, the given two ratios are in proportion. The answer is
The units in the ratio does not matter while comparison. So, we will ignore the units. The above statement can be represented as: 99: 45 = 44: 20
99/45 = (9 × 11)/ (9 × 5) = 11/5 Ratio = 11: 5
44/20 = (4 × 11)/ (4 × 5) Cancelling out the common factors, we get: = 11/5 Ratio = 11: 5 The given ratios are equal. Hence, the given two ratios are in proportion. The answer is
The units in the ratio does not matter while comparison. The above statement can be represented as: 32: 64 = 6: 12
32/64 = (32 × 1)/ (32 × 2) = 1/2 Ratio = 1: 2
6/12 = (6 × 1)/ (6 × 2) Cancelling out the common factors, we get: = 1/2 Ratio = 1: 2 The given ratios are equal. Hence, the given two ratios are in proportion. The answer is
The units in the ratio does not matter while comparison. So, we will ignore the units. The above statement can be represented as: 45: 60 = 12: 15
45/60 = (15 × 3)/ (15 × 4) = 3/4 Ratio = 3: 4
12/15 = (3 × 4)/ (3 × 5) Cancelling out the common factors, we get: = 4/5 Ratio = 4: 5 The given ratios are not equal. Hence, the given two ratios are not in proportion. The answer is
(a) 25 cm: 1 m and ₹ 40: ₹ 160
Middle terms: 1 m and ₹ 40 Extreme terms: 25 cm and ₹ 160
The units in the ratio does not matter while comparison. But, the units in a ratio should be the The above statement can be represented as: 25: 100 = 40: 160 1m = 100 cm We have converted the unit meter into centimetre. We can also convert the unit centimetre to meter. The answer at the end will be the same in both cases.
25/100 = (25 × 1)/ (25 × 4) Cancelling out the common factors, we get: = 1/4 Ratio = 1: 4
40/160 = (40 × 1)/ (40 × 4) Cancelling out the common factors, we get: = 1/4 Ratio = 1: 4 The given ratios are equal. Hence, the given two ratios are in proportion. The answer is
Middle terms: 65 litres and 6 bottles Extreme terms: 39 litres and 10 bottles
The units in the ratio does not matter while comparison. But, the units in a ratio should be the The above statement can be represented as: 39: 65 = 6: 10
39/65 = (13 × 3)/ (13 × 5) Cancelling out the common factors, we get: = 3/5 Ratio = 3: 5
6/10 = (2 × 3)/ (2 × 5) Cancelling out the common factors, we get: = 3/5 Ratio = 3: 5 The given ratios are equal. Hence, the given two ratios are in proportion. The answer is
The units in the ratio does not matter while comparison. But, the units in a ratio should be the The above statement can be represented as: 2: 80 = 25: 625
2/80 = (2 × 1)/ (2 × 40) Cancelling out the common factors, we get: = 1/40 Ratio = 1: 40
25/625 = (25 × 1)/ (25 × 25) Cancelling out the common factors, we get: = 1/25 Ratio = 1: 25 The given ratios are not equal. Hence, the given two ratios are not in proportion. The answer is
Middle terms: 2.5 litres and ₹ 4 Extreme terms: 200 ml and ₹ 50
The units in the ratio does not matter while comparison. But, the units in a ratio should be the The above statement can be represented as: 200: 2500 = 4: 50 1 Litre = 1000 Ml 2.5 litres = 2.5 × 1000 = 2500 millilitres Here, we have converted the litres into millilitres. We can also convert millilitres to litres. The answer in both the cases would be the same.
200/2500 = (100 × 2)/ (100 × 25) Cancelling out the common factors, we get: = 2/25 Ratio = 2: 25
4/50 = (2 × 2)/ (2 × 25) Cancelling out the common factors, we get: = 2/25 Ratio = 2: 25 The given ratios are equal. Hence, the given two ratios are in proportion. The answer is ## Exercise 12.3
Cost of 1 m of cloth = 1470/7 Cost of 1 m of cloth = ₹ 210 Cost of 5 m of cloth = 210 × 5 = ₹ 1050 Thus, the cost of 5m of cloth is rupees 1050.
Amount earned by Ekta in 1 day = ₹ 3000/10 = ₹ 300 Amount earned by Ekta in 30 days = Amount earned 1 day × 30 = 300 × 30 = 9000 Thus, Ekta earns rupees 9000 is 30 days.
The amount rained in 1 da = 276/3 = 92 mm The amount rained in 1 day = 92 mm The amount rained in 7 days = 92 × 7 = 644 mm The unit is in millimetres. But, according to the question, the unit should be in centimetres. So, we will convert mm to cm. 1 cm = 10 mm 1 mm = 1/10 cm 644 mm = 644/10 cm = 64.4 cm Thus, the amount rained in the 7 days is 64.4 cm.
Cost of 1 kg wheat = ₹ 91.50/5 = ₹ 18.30 Cost of 8 kg wheat = cost of 1 kg × 8 = ₹ 18.30 × 8 = ₹ 146.40
Total cost of wheat given = ₹ 183 The quantity of wheat purchased = Total quantity / Rate per kg = ₹ 183 /₹ 18.30 = (₹ 18.30 × 10)/ (₹ 18.30 × 1) = 10 Thus,
The temperature drop in 1 day = 15/30 = 1/2 = 0.5 degree Celsius The temperature drop in the next 10 days = 0.5 degree Celsius × 10 = 5 degree Celsius
Rent paid by Shaina for 3 months = ₹ 15000 Rent paid for 1 month = ₹ 15000/3 = ₹ 5000 Rent paid by Shaina for the whole year = ₹ 5000 × 12 = ₹ 60000
Rent paid by Shaina for 3 months = ₹ 15000 1 year = 12 months 3 × 4 = 12 Rent paid by Shaina for the whole year = Rent for 3 months × 4 = ₹ 15000 × 4 = ₹ 60000
Cost of 1 dozen bananas = ₹ 180/4 = ₹ 45 The bananas purchased in ₹ 90 = 90/Cost of 1 dozen bananas = 90/45 = 2 Thus, 2 dozen bananas can be purchased for ₹ 90. 1 dozen = 12 2 dozens = 12 × 2 2 dozens = 24 bananas
Weight of 1 book = 9/72 Weight of 1 book = 1/8 Weight of 40 books = 40 × weight of 1 book = 40 × 1/8 = 5 kg Thus, the weight of 40 books is 5 kg.
Diesel required for covering a distance of 1 km = 108/594 Factorizing the above ratio, = (54 × 2)/ (54 × 11) Cancelling out the common terms, we get: 2/11 Diesel required for covering a distance of 1650 km = 2/11 × 1650 = 300 litres Thus, 300 litres of diesel will be required by the truck to cover a distance of 1650 km.
Cost of 1 pen = 150/10 = ₹ 15 Cost of 7 pens purchased by Manish = ₹ 84 Cost of 1 pen = 84/7 = ₹ 12 Thus, Manish got the pens cheaper.
Runs made by Anish in 1 over = 42/6 = 7 runs Runs made by Anup in 7 overs = 63 Runs made by Anup in 1 over = 63/7 = 9 runs Thus, Anup made more runs per over. Next Topicclass 7 Maths |