RS Aggarwal Class 6 Maths Solutions Chapter 10- Ratio, Proportion And Unitary Method Exercise 10D

RS Aggarwal 2021-2022 for Class 6 Maths Solutions Chapter 10- Ratio, Proportion And Unitary Method

RS Aggarwal Class 6 Math Solution Chapter 10- Ratio, Proportion And Unitary Method, Exercise 10D is available here. RS Aggarwal Class 6 Math Solutions are solved by expert teachers in step by step, which help the students to understand easily.  RS Aggarwal textbooks are responsible for a strong foundation in Maths. These textbook solutions help students in exams as well as their daily homework routine. The solutions included are easy to understand, and each step in the solution is described to match the students’ understanding.

Rs Aggarwal Class 6 Math Solution Chapter 10- Ratio, Proportion And Unitary Method 

Exercise 10D

OBJECTIVE QUESTIONS

Mark (✓) against the correct answer in each of the following:

1. The ratio 92 : 115 in its simplest form is 

(a) 23 : 25

(b) 18 : 23

(c)  3 : 5

(d) 4 : 5

Solution: The correct option is (d) 4 : 5

92 : 115

`frac\{92}{115}`  =  `frac\{92 ​÷ 23}{115 ÷ 23}`   =  `frac\{4}{5}` 

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

(a) 95

(b) 76

(c)  114

(d) none of these

Solution: The correct option is (a) 95

Given :  

57 : x : : 51 : 85

We know:

Product of means = Product of extremes

51x = 57 × 85

x =   `frac\{cancel 4845^51}{cancel 51}`  = 95

3. If 25 : 35 : : 45 : x, then the value of x is 

(a) 63

(b) 72

(c)  54

(d) none of these

Solution: The correct option is (a) 63

Given :  

25 : 35 : : 45 : x

We know:

Product of extremes = Product of means 

25x = 35 × 45

x =   `frac\{cancel 1575^63}{cancel 25}`  = 63

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

(a) 42

(b) 32

(c)  28

(d) none of these

Solution: The correct option is (c) 28

Given :  

4 : 5 : : x : 35

We know:

Product of means = Product of extremes

5x = 4 × 35

x =   `frac\{cancel 140^28}{cancel 5}`  = 28

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

(a) ac = bd

(b) ad = bc

(c)  ab = cd

(d) none of these

Solution: The correct option is (b) ad = bc

a, b, c d are in proportion, such that we have:

  a : b : : c : d

Now, we know:

  Product of means = Product of extremes

                    b ​× c = a ​× d

                       bc = ad

6. If a, b, c are in proportion, then

(a) `a^2` = bc

(b) `b^2` = ac

(c)  `c^2` = ab

(d) none of these

Solution: The correct option is (b) `b^2` = ac

a, b, c are in proportion, such that we have:

  a : b : : b : c

Now, we know:

  Product of means = Product of extremes

                    b ​× b = a ​× c

                       `b^2` = ac

7. Choose the correct statement: 

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

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

(c)  two ratios cannot be compared

(d) none of these

Solution: The correct option is (b) (5 : 8) < (3 : 4)

`frac\{5}{8}` < `frac\{3}{4}`

⇒ 5 ​× 4 < 3 ​× 8

⇒ 20 < 24

8. If Rs. 760 is divided between A and B in the ratio 8 : 11, then B's share is 

(a) Rs 440

(b) Rs. 320

(c)  Rs. 430

(d) Rs. 330

Solution: The correct option is (a) Rs. 440

Total amount = Rs. 760

Rato of A : B = 8 : 11

So, Share of B's = `frac\{760 × 11}{8 + 11}`

          = `frac\{cancel 760^40 ​× 11}{cancel 19}`

         = Rs. 40  ​× 11

         = Rs. 440

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

(a) 85

(b) 119

(c) 105

(d) 147

Solution: The correct option is (d) 147

Let the two numbers be 5x and 7x.

A/q,

     5x + 7x = 252

    ⇒ 12x = 252

   ⇒ x = `frac\{cancel 252^21}{cancel 12}`

    ⇒ x = 21

Now, 5x = 5 ​× 21 = 105

        7x = 7 ​× 21 = 147

     The larger number is 147.

10. 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

Solution: The correct option is (b) 50 cm

Let the sides of a triangle be 1x, 3x and 5x.

A/q, 

  1x + 3x + 5x = 90

   ⇒ 9x = 90

   ⇒ x = `frac\{cancel 90^10}{cancel 9}`

   ∴ x = 10

Now the length of largest side = 5x = 5 ​× 10 = 50

11. 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) 1190

(b) 2380

(c) 2856

(d) 2142

Solution: The correct option is (c) 2856

Let the numbers of boys be 12x and girls be 5x.

A/q,

  5x = 840

  ⇒ x = 840

 ⇒  x = `frac\{cancel 840^168}{cancel 5}`

   ∴ x = 168

Number of boys = 12x = 12 × 168 = 2016

Number of girls = 5x = 5 × 168 = 840

Total strength of the school = 2016 + 840 = 2856

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

(a) Rs. 164

(b) Rs. 161

(c) Rs. 118.30

(d) Rs. 123.50

Solution: The correct option is (b) Rs. 161

Cost of 12 pens = Rs. 138

Cost of 1 pen  = `frac\{138}{12}`

Cost of 14 pens = `frac\{138 × 14}{12}`

                         = `frac\{cancel 1932^161}{cancel 12}`

 Cost of 14 pens = Rs. 161

13.  If 24 workers can build a wall in 15 days, how many days will 8 workers take to build a similar wall?

(a) 42 days

(b) 45 days

(c) 48 days

(d) none of these

Solution: The correct option is (b) 45 days

Time taken to built a wall by 24 workers = 15 days

Time taken to built a wall by 1 workers = 15 × 24 days

Time taken to built a wall by 8 workers = `frac\{15 × cancel 24^3}{cancel 8}` = 45 days

14. If 40 men can finish a piece of work in 26 days, how many men will be required to finish it in 20 days?

(a) 52

(b) 31

(c) 13

(d) 65

Solution: The correct option is (a) 52

Number of men works in 26 days = 40

Number of men works in 1 days = 40 × 26

Number of men works in 20 days = `frac\{cancel 40^2 × 26}{cancel 20}`

                                                      = 52 workers

15. In covering 111 km, a car consumes 6 L of petrol. How many kilometres will it go in 10 L petrol?

(a) 172 km

(b) 185 km

(c) 205 km

(d) 266.4 km

Solution: The correct option is (b) 185 km

Cover distance in 6 L of petrol = 111 km

Cover distance in 1 L of petrol = `frac\{111}{6}` km

Cover distance in 10 L of petrol = `frac\{111 × 10}{6}` km

                                                    = `frac\{cancel 1110^185}{cancel 6}`

Cover distance in 10 L of petrol = 185 km.

16. In a fort, 550 men had provisions for 28 days. How many days will it last for 700 men?

(a) 22 days

(b) 35`frac\{7}{11}` days

(c) 34 days

(d) none of these

Solution: The correct option is (a) 22 days

Provisions last for 550 men = 28 days

Provisions last for 1 men = 550 × 28 = 15400

Provisions last for 700 men = `frac\{cancel 15400^22}{cancel 700}`

                                            = 22 days

17. The angles of a triangle are in the ratio 3 : 1 : 2. The measure of the largest angle is

(a) 30°

(b) 60°

(c) 90°

(d) 120°

Solution: The correct option is (c) 90°

Let  the three angles be (3x)°, (1x)° and (2x)°.

We know, the sum of the angles of a triangle is 180°.

        3x + 1x + 2x = 180°

      ⇒ 6x = 180°

​      ⇒ x =  `frac\{cancel 180^30}{cancel 6}`  

        ∴ x = 30°

∴  (3x )° = (3 ​× 30)° = 90°

​     (1x)° = (1​ × 30)° = 30°

​     (2x)° = (2 × 30)° = 60°

The measure of the largest angle is 90°​.

18. Length and breadth of a rectangular field are in the ratio 5 : 4. If the width of the field is 36 m, what is its length?

(a) 40 m

(b) 45 m

(c) 54 m

(d) 50 m

Solution: The correct option is (b) 45 m

Let the length and the breadth be 5x and 4x, respectively.

Now , 4x = 36

     x =  `frac\{cancel 36^9}{cancel 4}`  

= 9

Length = 5x = 5 × 9 = 45 m

19. If a bus covers 195 km in 3 hours and a train covers 300 km in 4 hours, then the ratio of their speeds is 

(a) 13 : 15

(b) 15 : 13

(c) 13 : 12

(d) 12 : 13

Solution: The correct option is (a) 13 : 15

Speed of the bus = `frac\{distance}{time}`

            = `frac\{cancel 195^65}{cancel 3}`

           = 65 km/hr

Speed of the train =  `frac\{distance}{time}`

             = `frac\{cancel 300^75}{cancel 4}`

            = 75 km/hr

Ratio of their speed = `frac\{65}{75}`  

= `frac\{cancel 65^13}{cancel 75^15}` 

= `frac\{13}{15}` = 13 : 15

20. If the cost of 5 bars of shop is Rs, 82.50, then the cost of one dozen such bars is 

(a) Rs. 208

(b) Rs. 192

(c) Rs. 198

(d) Rs. 204

Solution: The correct option is (c) Rs. 198

Cost of 5 bars of soap = Rs 82.50

Cost of 1 bar of soap =  `frac\{82.50}{5}`  = Rs 16.5

Cost of 12 (1 dozen) bars of soap = 16.5 × 12 = Rs 198

21. If the cost of 30 packets of 8 pencils each is Rs. 600, what is the cost of 25 packets of 12 pencils each?

(a) Rs. 725

(b) Rs. 750

(c) Rs. 480

(d) Rs. 720

Solution: The correct option is (b) Rs. 750

Total pencils in 30 packets of 8 pencils = 30 × 8 = 240

Total pencils in 25 packets of 12 pencils = 25 × 12 = 300

Now, 

Cost of 240 pencils = Rs. 600

Cost of 1 pencils = `frac\{600}{240}`

Cost of 300 pencils = `frac\{600 × 300}{240}`

                                = `frac\{cancel 180000^750}{cancel 240}`

                                = Rs. 750

22. A rail journey of 75 km costs Rs. 215. How much will a journey of 120 km cost?

(a) Rs. 344

(b) Rs. 324

(c) Rs. 268.75

(d) none of these

Solution: The correct option is (a) Rs. 344

Cost of rail journey of 75 km = Rs 215

Cost of rail journey of 1 km = Rs  `frac\{215}{75}` 

Cost of rail journey of 120 km = `frac\{120​ ×  215}{75}`   

                         = `frac\{cancel 25800^344}{cancel 75}` 

                         = Rs 344

23. The 1st, 2nd and 4th terms of a proportion are 12, 21 and 14 respectively. Its third term is

(a) 16

(b) 18

(c) 21

(d) 8

Solution: The correct option is (d) 8

Let the third term be x.

Then, we have:

12 : 21 : : x : 14

We know:

    Product of means = Product of extremes

      21x = 12 × 14

  ⇒ 21x = 168

  ⇒ x =  `frac\{cancel 168^8}{cancel 21}`  

        = 8

The third term is 8

24. 10 boys can dig a pitch in 12 hours. How long will 8 boys take to do it?

(a) 9 h 36 min

(b) 15 h

(c) 6 h 40 min

(d) 13 h 20 min

Solution: The correct option is (b) 15 hrs.

Time taken by 10 boys to dig a pitch = 12 hours

Time taken by 1 boy to dig a pitch = 12 × 10 = 120 hours 

Time taken by 8 boys to dig a pitch =  `frac\{120}{8}` = 15 hours