R s aggarwal solutions mathematics class 6 Solutions for Chapter 10 ratio proportion and unitary method.

Find each of the following ratios in the simplest form:

(i) 24 to 56

(ii) 84 paise to Rupees 3

(iii) 4 Kg to 750 g

(iv) 1.8 Kg to 6 Kg

(v) 48 Minutes to 1 hour

(vi) 2.4 Km to 900 m

Express each of the following ratios in the simplest from:

(i) 36 : 90

(ii) 324 : 144

(iii) 85 : 561

(iv) 480 : 384

(v) 186 : 403

(vi) 777 : 1147

Write each of the following ratios in the simplest from:

(i) Rupees 6.30 : Rupees 16.80

(ii) 3 weeks : 30 days

(iii) 3 m 5 cm : 35 cm

(iv) 48 min : 2 hrs 40 min

(v) 1 L 35 mL : 270 mL

(vi) 4 kg : 2 kg 500 g

Mr. Sahai and his wife are both school teachers and earn rupees 16,800 and 10,500 per month

respectively. Find the ratio of

(i) Mr. Sahai’s income to his wife’s income;

(ii) Mrs. Sahai’s income to her husband’s income;

(iii) Mr. Sahai’s to the total income of the two.

Rohit earns Rupees 15,300 and saves Rupees 1,224 per month. Find the ratio of

(i) his income and savings;

(ii) his income and expenditure;

(iii) his expenditure and savings.

The ratio of the number of males and females in a textile mill is 5:3. If there are 115 male workers, what is the number of female workers in the mill?

The boys and girls in a school are in the ratio 9: 5. If the total strength of the school is 448, find the number of girls.

Divide Rupees 1,575 between Kamal and Madhu in the ratio 7: 2.

Divide Rupees 3,450 among A, B, and C in the ratio 3: 5: 7.

Two numbers are in the ratio 11: 12 and their sum is 460. Find the numbers.

Determine if the following numbers are in proportion:

(i) 4, 6, 8, 12

(ii) 7, 42, 13, 78

(iii) 33, 121, 9, 96

(iv) 22, 33, 42, 63

(v) 32, 48, 70, 210

(vi) 150, 200, 250, 300

Verify the following:

(i) 60 : 105 : : 84 : 147

(ii) 91 : 104 : : 119 : 136

(iii) 108 : 72 : : 129 : 86

(iv) 39 : 65 : : 141 : 235

Find the value of x in each of the following proportions:

(i) 55 : 11 : : x : 6

(ii) 27 : x : : 63 : 84

(iii) 51 : 85 : : 57 : x

(iv) x : 92 : : 87 : 116

Write (T) for true and (F) for false in each of the following:

(i) 51 : 68 : : 85 : 102

(ii) 36 : 45 : : 80 : 100

(iii) 30 bags : 18 bags : : Rupees 450 : Rupees 270

(iv) 81 Kg : 45 Kg : : 18 men : 10 men

(v) 45 Km : 60 Km : : 12 h : 15 h

(vi) 32 Kg : Rupees 36 : : 8 Kg : Rupees 9

Determine if the following ratios form a proportion:

(i) 25 cm: 1m and Rupees 40: Rupees 160

(ii) 39 liters: 65 liters and 6 bottles: 10 bottles

(iii) 200 mL: 2.5 L and Rupees 4: Rupees 50

(iv) 2 Kg: 80 Kg and 25 g: 625 Kg

In proportion, the 1st, 2nd, and 4th terms are 51, 68, and 108 respectively. Find the 3rd term.

If the cost of 14 m of cloth is Rupees 1,890, find the cost of 6 m of cloth.

If the cost of a dozen soaps is rupees 285.60 what will the cost of 15 such soaps?

If 9 Kg of rice costs Rupees 327.60, what will be the cost of 50 Kg of rice?

If 22.5 m of a uniform iron rod weighs 85.5 Kg, what will be the weight of 5 m of the same rod?

If 15 tins of the same size contain 234 Kg of oil, how much oil will there be in 10 such tins?

If 12 L of diesel is consumed by a car in covering a distance of 222 Km, how many kilometers will it go 22 L of diesel?

Transport charges 540 to carry 25 Tonnes of weight. What will it charge to carry 35 tonnes?

4.5 g of an alloy of copper and zinc contains 3.5 g of copper. What weight of copper will there be in 18.9 g of the alloy?

35 inland letters cost Rupees 87.50. How many such letters can we buy for Rupees 315?

The cost of 4 dozen bananas is Rupees 104. How many bananas can be purchased for Rupees 6.50?

The ratio 92 : 115 in its simplest form is

(a) 23 : 25

(b) 18 : 23

(c) 3 : 5

(d) 4 : 5

If 57 : x : : 51 : 85, then the value of x is

(a) 95

(b) 76

(c) 114

(d) none of these

If 4 : 5 : : x : 35, then the value of x is

(a) 42

(b) 32

(c) 28

(d) none of these

If a, b, c, d are in proportion, then

(a) ac = bd

(b) ad = bc

(c) ab = cd

(d) none of these

If a, b, c are in proportion, then

(a)a^2= bc

(b)b^2= ac

(c)c^2= ab

(d) none of these

Choose the correct statement:

(a) (5 : 8) > (3 : 4)

(b) (5 : 8) < (3 : 4)

(c) two ratios cannot be compared

If Rupees 760 is divided between A and B in the ratio 8: 11, then B’s share is

(a) Rupees 440

(b) Rupees 320

(c) Rupees 430

(d) Rupees 330

Two numbers are in the ratio 5 : 7 and the sum of these numbers is 252. The larger of these numbers is

(a) 85

(b) 119

(c) 105

(d) 147

The sides of a triangle are in the ratio 1 : 3: 5 and its perimeter is 90 cm. The length of its largest side is

(a) 40 cm

(b) 50 cm

(c) 36 cm

(d) 54 cm

The ratio of boys and girls in a school is 12: 5. If the number of girls is 840, the total strength of the school is

(a) 1,190

(b) 2,380

(c) 2,856

(d) 2,142

If the cost of 12 pens is Rupees 138, then the cost of 14 such pens is

(a) Rupees 164

(b) Rupees 161

(c) Rupees 118.30

(d) Rupees 123.50