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The correct option is indicated by (√) mark with explanation in the rightmost column

**Ratio & Proportion MCQ**

**1. Inverse Ratio of a : b is**

(a)

(b) a : a

(c) b : a

(d) Both b & c

Inverse ratio of a : b is b : a**. **So, option **(c)** is correct

**2. Sub-duplicate ratio of a : b is:**

(a) a^{2} : b^{2}

(b) √a^{3} : √b^{3}

(c) √a : √b

(d)

Sub-duplicate ratio of a : b is Öa : Öb. So, option **(c)** is correct

**3. If A, B and C started a business by investing Rs. 1, 26,000, Rs. 84.000 and Rs. 2.10.000. If at the end of the year profit is Rs. 2.42.000 then the share of each is:**

(a) 72.600, 48.400, 1.21.000

(b) 48.400, 1.21.000, 73.000

(c) 73.000, 49.000, 120.000

(d) 48.600, 1.21.400, 72.000

Ratio of capital A: B: C = 126000: 84000: 210000 = 126: 84: 210 = 3: 2: 5.

Let us assume, Capital of A=3x, B=2x, C=5x

So, 3x + 2x + 5x = 242000, Or, 10x = 242000, Or, x = 24,200

So, A’s share 24,200 x 3 = 72600, B’s share 24200 x 2 =48400, C’s share 24200 x 5 = 121000.

So, Option **(a)** is correct

**4. a: b is equal to **

(a) a^{2}:b^{2}

(b) a^{3}:b^{3}

(c) b:a

(d) None of these.

None of the ratio specified in option (a) to (c) are equal to the ratio a:b. So, option **(d)** is correct

**5. If a : b = c : d then b : a = d : c, the property of proportion is called:**

(a) Invertendo

(b) Alternendo

(c) Dividendo

(d) The statement is false

According to Invertendo rule, If a : b = c : d then b : a = d : c. So, option **(a)** is correct

**6. If a : b = c : d then a ****–**** b : b = c ****–**** d : d, property of proportion is called:**

(a) Dividendo

(b) Alternendo

(c) Componendo

(d) Invertendo

According to dividendo rule, if a : b = c : d, Then (a – b) : b = (c – d) : d. So, Option **(a)** is correct

**7. The ratio of x : y is 7 : 9 and y : z is 6 : 7. The ratio of x : z is:**

(a) 2 : 3

(b) 3 : 4

(c) 3 : 1

(d) 2 : 1

So, x:z=2:3. So, Option **(a)** is correct

**8. A, B, C, D are four numbers so that A : B = 2 : 3, B : C = 4 : 5, C : D = 5 : 8, then A : D is:**

(a) 2 : 5

(b) 3 : 4

(c) 1 : 3

(d) 2 : 1.

So, Option **(c)** is correct

**9. The fourth proportional to 3,4 and 15 is:**

(a) 20

(b) 60

(c) 21

(d) 12.

Let fourth proportion=x .

So, Option **(a)** is correct

**10. The sum of the squares of three numbers is 116 and their ratio is 2:3:4. The numbers are:**

(a) 10, 15, 20

(b) 4,6,8

(c) 2,9,19

(d) 6,12,16.

Let three numbers be 2x, 3x, 4x. So, (2x)^{2} + (3x)^{2} + (4x)^{2} = 116

Hence, Three numbers are : (2 x 2), (3 x 2), (4 x 2) = 4, 6, 8. So, Option **(b)** is correct

**11. The ratio of the number of boys and girls in a school is 2 : 5. If there are 350 students in the school, the numbers of girls in the school are:**

(a) 220

(b) 125

(c) 210

(d) 250.

Let Number of boys is 2n, and Number of girls is 5n.

Number of girls in the school = 50 x 5 = 250. So, Option **(d)** is correct

**12. Pencils, pens and exercise books in a shop are in the ratio of 10:2:3. If there are 120 pencils, the number of exercise books in the shop is:**

(a) 36

(b) 42

(c) 40

(d) 120.

Let number of : pencils = 10x, Pens = 2x , Exercise books = 3x. So, 10x = 120, or x = 12

So, Number of exercise book = 3 x 12 = 36. So, Option **(a)** is correct

**13. The third proportional to (x ^{2 }**

**–**

**y**

^{2}) and (x**–**

**y) is:**

(a)

(b)

(c) x+y

(d) None of the above

Let third proportional be P.

So, Option **(b)** is correct

**14. If x/2y=3/2, find the value of (2x+y) / (x-2y)**

(a) 1/7

(b) 7.

(c) 8

(d) 12.

So, Option **(b)** is correct

**15. The fourth proportional to 4, 6, 8 is:**

(a) 12

(b) 24

(c) 42

(d) 16.

Let fourth proportional be x ,

So, Option **(a)** is correct

**16. The third proportional to 12, 18 is:**

(a) 21

(b) 27

(c) 32

(d) 54.

Let third population be x,

So, Option **(b)** is correct

**17. The mean proportional between 25, 81 is:**

(a) 54

(b) 20

(c) 45

(d) 30.

Let mean population be x.

So, Option **(c)** is correct

**18. If A : B = 3 : 2 and B : C = 3 : 5, then A : B : C is**

(a) 9 : 6 : 10

(b) 3 : 6 : 5

(c) 10 : 9 : 6

(d) 4 : 9 : 8

So, Option **(a)** is correct

**19. If x : y = 2 : 3, y : z = 4 : 3 then x : y : z is:**

(a) 1 : 3 : 4

(b) 4 : 3 : 6

(c) 3 : 2 : 4

(d) 8 : 12 : 9.

So, x : y : z = 8 : 12 : 9.

So, Option **(d)** is correct

**20. Division of Rs. 750 into 3 parts in the ratio 4 : 5 : 6 is: **

(a) (200, 250, 300)

(b) (250, 250, 250)

(c) (350, 250, 150)

(d) (200, 450, 300)

Let three parts be 4x, 5x and 6x. So, 4x + 5x + 6x = 750, Or, 15x = 750, Or, x = 50,

So, 3 parts are : 4 x 50 = 200, 5 x 50 = 250 and 6 x 50 = 300. So, Option **(a)** is correct

**21. The sum of the ages of 3 persons is 150 years. 10 years ago their ages were in the ratio 7 : 8 : 9. Their present ages are:**

(a) (45, 50, 55)

(b) (40, 60, 50)

(c) (35, 45, 70)

(d) Any of these

Let 10 years ago age of the three persons be : 7x, 8x, 9x. So, ** **7x + 8x + 9x + ( 10 x 3) = 150,

So, their present Ages are : 7 x 5 = 35 + 10 = 45, 8 x 5 = 40 + 10 = 50, 9 x 5 = 45 + 10 = 55 years.

So, Option **(a)** is correct

**22. The numbers 12, 16, x, 20 are in proportion. Value of x =**

(a) 24

(b) 20

(c) 15

(d) 12

So, Option **(c)** is correct

**23. Two numbers are in the ratio 3 : 4. If 6 be added to each terms of the ratio, then the new ratio will be 4 : 5, then the numbers are:**

(a) 16 & 30

(b) 17, 19

(c) 18 and 24

(d) 12 & 20

Or, 16x – 15x = 30 – 24 = 6 , Or, x = 6.

So, the numbers are 3 x 6=18, and 4 x 6=24. So, Option **(c)** is correct.

So, Option **(a)** is correct

**25. If A : B = 2 : 3, B : C = 1 : 2, find A : C**

(a) 1 : 3

(b) 1 : 2

(c) 6 : 1

(d) 1 : 5

So, Option **(a)** is correct

**26. If x is the mean proportional of x ****–**** 2 and x ****+** **6, find the value of x.**

(a) 5

(b) 2

(c) 3

(d) 6

(x – 2), x, (x + 6) are in proportion. So, (x-2) / x = x/ (x-6), Or, (x – 2) (x + 6) = x^{2}.

Or, x^{2 }– 2x + 6x – 12 = x^{2}, Or, x^{2 }+ 4x – 12 – x^{2 }= 0, Or, 4x – 12= 0, Or, 4x = 12 or, x= 3.

So, Option **(c)** is correct

**27. The ratio between the ages of Kanika and Moni is 6 : 5 and the sum of their ages is 44 years. Find the ratio of their ages after 8 years?**

(a) 2 : 5

(b) 8 : 7

(c) 4 : 3

(d) 6 : 5

Let current age of Kanika = 6x, current age of Moni = 5x, So, 6x + 5x = 44. Or, 11x = 44, or, x = 4.

So, Current age of Konika = 6 x 4 = 24 years, and Current age of Moni = 5 x 4 = 20 years

After 8 years : Konika will be = 24 + 8 = 32 years, Moni will be = 20 + 8 = 28 years

Ratio of Age would be = 32 : 28 = 8 : 7. So, Option **(b)** is correct

**28. Two numbers are in the ratio 5 : 6, when 4 is subtracted from each, the ratio becomes 4:5. Find the greatest number**

(a) 24

(b) 28

(c) 22

(d) 16

Let one number be 5x. and Other number be 6x

Or, 25x – 20 = 24x – 16, Or, 25x – 24x = – 16 + 20 = 4, Or, x = 4,

So, greatest number is 6 x 4 = 24. So, Option **(a)** is correct

**29. Two numbers are in the ratio 2: 3 and the difference of their squares is 320. The numbers are:**

(a) 14 & 20

(b) 16 & 24

(c) 18 & 24

(d) 10 & 24

Let two numbers be 2x & 3x. So, (3x)^{2} – (2x)^{2} = 320, Or, 9x^{2} – 4x^{2} = 320.

So, the Numbers are (2 x 8) = 16 & (3 x 8) = 24.

So, Option **(b)** is correct

**30. An alloy is to contain copper and zinc in the ratio 9: 4. The zinc required to melt with 24kg of copper is:**

(a) 10^{2}/_{3}Kg

(b) 10^{3}/_{5}Kg

(c) 10^{1}/_{2}Kg

(d) 10Kg

In the alloy, Let copper be 9x and zinc be 4x.

So, Option **(a)** is correct

**31. Two numbers are in the ratio 7: 8. If 3 is added to each of them, their ratio becomes 8: 9. The numbers are:**

(a) 32,45

(b) 24,27

(c) 21,24

(d) 25,35

So, the Two numbers are (7 x 3) = 21 & (8 x 3) = 24. So, Option **(c)** is correct

**32. A box contains Rs.56 in the form of coins of one rupee, 50 paise and 25 paise. The number of 50 paise coin is double the number of 25 paise coins and four times the numbers of one rupee coins. The numbers of 50 paise coins in the box is.**

(a) 64

(b) 28

(c) 30

(d) 24

Number of 50 paise coins = 4 x 16 = 64. So, Option **(a)** is correct

**33. Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally entire cost of the car, then the share of each of the remaining persons increased by:**

(a) 1/6

(b) – 1/10

(c) 1/7

(d) 1/56

When Eight persons are sharing equally, then each share =

When seven persons are sharing equally, then each share =

So, Increase in share of remaining persons

So, Option **(d)** is correct

**34. A bag contains Rs.187 in the form of 1 rupee, 50 paise and 10 paise coins in the ratio 3: 4: 5. Find the number of each type of coins:**

(a) 102. 136. 170

(b) 136. 102. 170

(c) 102. 115. 175

(d) 70. 115. 182

Let 3x be the number of 1 rupee coin.

5x be the number of 10 paise coins.

So,

So, 1 Rupee coins = 3 X 34 = 102, 50 paise coins = 4 X 34 = 136, 10 paise coins = 5 X 34 = 170

So, Option **(a)** is correct

**35. P, Q and R are three cities. The ratio of average temperature between P and Q is 11: 12 and that between P and R is 9: 8. The ratio between the average temperature of Q and R is:**

(a) 22: 27

(b) 27: 22

(c) 30: 35

(d) 24: 27

or, Q: R = 27: 22. So, Option **(b)** is correct

**36. Rs.407 are to be divided among A, B and C so that their shares are in the ratio 1/4: 1/5:1/6. The respective shares of A, B, C are:**

(a) Rs.165, Rs.132, Rs.110 (b) Rs.170, Rs.110, Rs.142 (c) Rs.132, Rs.110, Rs.125 (d) Rs.110, Rs.142, Rs.152 |

So, Option **(a)** is correct

**37. The incomes of A and B are in the ratio 3: 2 and their expenditures in the ratio 5: 3. If each saves Rs.1.500, then B’s income is:**

(a) Rs.6.000

(b) Rs.4.000

(c) Rs.9.000

(d) Rs.5.000

Let Income of A = 3x, B=2x, Expenditure of A=5y, B=3y

So, 3x – 5y = 1500 ……. (1), 2x – 3y = 1500 ……..(2)

Multiply equ. (1) By 2 : 6x – 10y = 3000

Multiply equ. (2) By 3 : 6x – 9y = 4500

Eq (1) – Eq (2) : – y = – 1500, Or, y = 1500,

Putting the value of y in Eq (1), we get, 3x = 1500 + (5 x 1500) = 1500 + 7500 = 9000. Or, 3x = 9000, Or, x = 3000. So, B’s Income = 2 x 3000 = Rs.6000. So, Option **(a)** is correct

**38. In 80 liters mixture of glycerin and water, the ratio of glycerin and water is 3: 1. The quantity of water added in the mixture in order to make this ratio 2: 1 is:**

(a) 30 liters

(b) 20 liters

(c) 18 liters

(d) 10 liters

Glycerin in 80 liter mixture = ¾ x 80 = 60 liter, Water in 80 liter mixture = ¼ x 80 = 20 liter

Let x liter water mixed.

Or, 2x = 20, Or, x = 10, 10 liter water should be mixed. So, Option **(d)** is correct

**39. The third proportional between (a ^{2} – b^{2}) and (a + b)^{2} is:**

(a) a + b/ (a – b)^{2}

(b) (a – b)^{2}/ (a + b)

(c) (a – b)^{3} / (a + b)

(d) (a + b)^{3} / (a – b)

Let third proportion be x. So, (a^{2} – b^{2}) /(a + b)^{2} = (a + b)^{2} / x,

or x=[(a + b) (a + b) (a + b) (a + b)] / (a^{2} – b^{2})

= [(a + b) (a + b) (a + b) (a + b)] / [(a– b) (a+b)] = (a– b)^{3} / (a-b). So, Option **(d)** is correct

**40. In what ratio should coffee worth Rs.10 per kg be mixed with coffee worth Rs.14 per kg, so that the average price of the mixture may be Rs.11 per kg?**

(a) 5: 7

(b) 3: 1

(c) 10: 11

(d) 3: 5

Let x kg coffee of Rs.10 per kg coffee should be mixed milk y kg coffee of Rs.14 per kg coffee

So, 10x + 14y = 11(x + y), Or, 10x + 14y = 11 x + 11y

So, x:y=3:1.

So, Option **(b)** is correct

**41. The age’s average of two persons are in the ratio 5: 7. Eighteen years ago their ages were in the ratio of 8: 13, their person ages (in years) are:**

(a) 50 ,70

(b) 60, 84

(c) 40, 56

(d) 30, 42

Let age of first person be 5x and age of second person be 7x

Or, 65x – 56x = 234 – 144 = 90, Or, 9x = 90, Or, x = 10

Present age first person 5X10 = 50 years & Second person 7X10 = 70 years. So, Option **(a)** is correct