Ratio & Proportion Questions - gkquestionsguru.com

51. If 20% of A = 30% of B = 1/6 of C, then find A ∶ B ∶ C.

यदि A का 20% = B का 30% = C का 1/6, तो A ∶ B ∶ C ज्ञात कीजिए।

12 ∶ 15 ∶ 18
15 ∶ 10 ∶ 18
15 ∶ 12 ∶ 18
18 ∶ 10 ∶ 12

Option”B” is correct

20% of A = 30% of B = 1/6 of C

⇒ 20/100 × A = 30/100 × B = 1/6 × C

⇒ A/5 = 3B/10 = C/6

⇒ A ∶ B ∶ C = 5 ∶ 10/3 ∶ 6 = 15 ∶ 10 ∶ 18

∴ A ∶ B ∶ C is 15 ∶ 10 ∶ 18.

52. If (x – a) ∶ (x – b) ∶ (x – c) = 10 ∶ 11 ∶ 12 and 2x = a + b + c, then find a ∶ b ∶ c.

यदि (x – a) ∶ (x – b) ∶ (x – c) = 10 ∶ 11 ∶ 12 है और 2x = a + b + c है, तो a ∶ b ∶ c का मान होगा-

23 ∶ 21 ∶ 22
23 ∶ 22 ∶ 21
21 ∶ 22 ∶ 23
22 ∶ 23 ∶ 21

Option”B” is correct

(x – a) ∶ (x – b) ∶ (x – c) = 10 ∶ 11 ∶ 12 and 2x = a + b + c,

⇒ (x – a) = (a + b + c) /2 – a = (b + c – a) /2 = 10 —- 1

⇒ (x – b) = (a + b + c) /2 – b = (a + c – b) /2 = 11 —- 2

⇒ (x – c) = (a + b + c) /2 – c = (a + b – c) /2 = 12 —- 3

From equation 2 and 3,

⇒ (a + c – b) = 22

⇒ (a + b – c) = 24

⇒ a = 23

Similarly, b = 22 and c = 21

∴ a ∶ b ∶ c = 23 ∶ 22 ∶ 21

53. x, y, and z are three positive numbers such that x > y > z. If the difference and the sum of x and y are in the ratio 1 ∶ 7 and that of y and z is in the ratio 1 ∶ 3, then find the ratio x ∶ z.

x, y और z तीन धनात्मक संख्याएँ हैं जिसमें कि x > y > z है। यदि x व y के अंतर और योग का अनुपात 1 : 7 है। इसी प्रकार y व z के अंतर और योग का अनुपात 1 : 3 है, तो x ∶ z का अनुपात ज्ञात कीजिए।

9 ∶ 4
8 ∶ 3
7 ∶ 2
6 ∶ 1

Option”B” is correct

Difference and sum of x and y are in ratio 1 ∶ 7,

⇒ (x – y)/(x + y) = 1/7

⇒ 7x – 7y = x + y

⇒ 6x = 8y

⇒ y = 3x/4 —-(1)

Also,

Difference and sum of y and z are in ratio 1 ∶ 3,

⇒ (y – z)/(y + z) = 1/3

⇒ 3y – 3z = y + z

⇒ 2y = 4z

⇒ y = 2z

Substituting from (1),

⇒ 3x/4 = 2z

⇒ x/z = 8/3

∴ Required ratio = x ∶ z = 8 ∶ 3

54. The ratio of apples, oranges and mangoes is 1/3 ∶ 1/5 ∶ 1/4. If 10% of apples, 25% of oranges and 30% of mangoes are sold, then find the remaining ratio of apples, oranges and mangoes.

सेब, संतरे और आमों का अनुपात 1/3 ∶ 1/5 ∶ 1/4 है। यदि 10% सेब, 25% संतरे और 30% आम बेचे जाते हैं, तो शेष सेब, संतरे और आमों का अनुपात ज्ञात कीजिए।

14 ∶ 6 ∶ 7
11 ∶ 6 ∶ 7
10 ∶ 6 ∶ 7
12 ∶ 6 ∶ 7

Option”D” is correct

Ratio of apples, oranges and mangoes = 1/3 ∶ 1/5 ∶ 1/4 = 60/3 ∶ 60/5 ∶ 60/4 = 20 ∶ 12 ∶ 15

Let the number of apples, oranges and mangoes be 200x, 120x and 150x.

According to the question

Remaining ratio of apples, oranges and mangoes = 200x × [90/100] ∶ 120x × [75/100] ∶ 150x × [70/100] = 180x ∶ 90x ∶ 105x = 12 ∶ 6 ∶ 7

55. There are a certain number of Rs. 10, Rs. 20 and Rs. 50 notes available in a box. The ratio of the number of notes of Rs. 10, Rs. 20 and Rs. 50 is 3 ∶ 4 ∶ 6. The total amount available in a box is Rs. 2460. The amount of Rs. 10 and Rs. 50 in a box is –

एक बॉक्स में 10 रूपए, 20 रूपए और 50 रूपए के कुछ नोट हैं। 10, 20 और 50 रूपए के नोटों का अनुपात 3 ∶ 4 ∶ 6 है। बॉक्स में कुल 2460 रूपए हैं। बॉक्स में 10 और 50 रूपए के नोटों की कुल राशि कितनी है –

Rs. 1980
Rs. 1250
Rs. 2300
Rs. 1760

Option”A” is correct

Let the number of notes of Rs. 10, Rs. 20 and Rs. 50 be 3a, 4a and 6a respectively.

Given,

⇒ 10 × 3a + 20 × 4a + 50 × 6a = 2460

⇒ 410a = 2460

⇒ a = 6

Number of notes of Rs. 10 = 3 × 6 = 18

Number of Notes of Rs. 20 = 4 × 6 = 24

Number of notes of Rs. 50 = 6 × 6 = 36

Required amount = 10 × 18 + 50 × 36 = Rs. 1980

56. The ratio of the incomes of A and B is 3 : 5, whereas the ratio of their expenditures is 4 : 7 respectively. If A and B save Rs. 16,000 and Rs. 26,000, respectively, then what is the difference (in Rs.) between their expenditures?

A और B की आय का अनुपात 3 : 5 है, जबकि उनके व्यय का अनुपात क्रमशः 4 : 7 है। यदि A और B क्रमशः 16,000 रुपये और 26,000 रुपये की बचत करते हैं, तो उनके व्यय के बीच अंतर (रुपये में) कितना है?

5000
6000
5400
6800

Option”B” is correct

Income ratio of A and B = 3x : 5x

Expenditure ratio of A and B = 4y : 7y

Savings of A = Rs. 16000

Savings of B = Rs. 26000

Concept used:

We will be using the concept of ratio.

Income = Expediuture + Saving

Calculation:

According to the question,

3x – 4y = 16000 —-(1)

5x – 7y = 26000 —-(2)

Subtract equation (1) from equation (2) after multiply by 5 in equation (1) and multiply by 3 in equation (2)

y = 2000

Difference between the expenditure are = 7y – 4y = 3y = 3 × 2000 = 6000

∴ The correct answer is 6000.

57. The ratio of tables and chairs in a room is 7 : 9. If there are 560 tables and chairs in the room, then what is the number of chairs ?

Option”A” is correct

Given

The ratio of table and chairs = 7 : 9

number of tables and chairs = 560

Concept Used:

Concept of ratio and proportion

Calculation Used

Let the number of table and chair be 7x and 9x ‘

Total number of chair and table = 560

Accordingly,

16x = 560

⇒ x = 35

Number of chair = 9x = 9 × 35 = 315

∴ The number of chair is 315

58. If P : Q = 5 : 2, then (2P – 3Q) : (3P – 5Q) is equal to:

यदि P: Q = 5: 2, तो (2P – 3Q): (3P – 5Q) किसके बराबर है:

5 : 6
2 : 7
4 : 5
3 : 4

Option”C” is correct

Given:

P : Q = 5 : 2

Calculation:

Suppose P = 5k, Q = 2k

⇒ (2P – 3Q) : (3P – 5Q) = 2(5k) – 3(2k) : 3(5k) – 5(2k)

= 10k – 6k : 15k – 10k

= 4k : 5k

= 4 : 5

59.Directions: Select the correct alternative from the given choices.

There are three employees – A, B and C in a department along with their boss. The ratio of the number of working days of A in a month to the number of non-working days of his boss in that month is 10 : 11. The total number of working days for B and C in that month is 43. The total number of days in that month is 30. The ratio of non-working days for C to the working days of B is 12 : 25. The ratio of working days of A and B is 4 : 5. Find the average of their non-working days.

निर्देश: दिए गए विकल्पों में से सही विकल्प का चयन कीजिए।
उनके विभाग में तीन कर्मचारी हैं – A, B और C, उनके बॉस के साथ। एक महीने में A के कार्य दिवसों की संख्या से उस महीने में उसके बॉस के गैर-कार्य दिवसों की संख्या का अनुपात 10 : 11. है। उस महीने में B और C के लिए कार्य दिवसों की कुल संख्या 43 है। उस महीने में दिनों की संख्या 30 है। C के लिए गैर-कार्य दिवसों से B के कार्य दिवसों का अनुपात 12 : 25 है। A और B के कार्य दिवसों का अनुपात 4 : 5 है। उनके गैर-कार्य दिवसों का औसत ज्ञात कीजिए।

49/3
49/4
50/4
51/4

Option”B” is correct

Let the number of working days of A, B, C and the boss be a, b, c and d respectively.

a/(30 – d) = 10/11

b + c = 43

(30 – c)/b = 12/25

[30 –(43 – b)]/b = 12/25

(b – 13)/b = 12/25

b = 25

c = 43 – b = 43 – 25 = 18

The ratio of working days of A and B is 4 : 5.

Hence, number of working days for A is 20.

a/(30 – d) = 10/11

d = 8

The working days for A, B, C and boss is 20, 25, 18 and 8 respectively.

Therefore, the non-working days for A, B, C and boss is 10, 5, 12 and 22 respectively.

The average is (10 + 5 + 12 + 22)/4 = 49/4

60. If l : m : n = 1 : 2 : 4, then $\sqrt{\frac{5 l^{2} + m^{2} + n^{2}}{l^{2}}}$ is equal to:

Option”D” is correct

⇒ l : m : n = 1 : 2 : 4

Now,

$\sqrt{\frac{5 l^{2} + m^{2} + n^{2}}{l^{2}}}$

$\Rightarrow \sqrt{\frac{5 \times 1^{2} + 2^{2} + 4^{2}}{1^{2}}}$

⇒ √(5 + 4 + 16)

⇒ √25

⇒ 5

Pages: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

7 thoughts on “Ratio & Proportion Questions”

Soni
18 January 2024 at 06:36

Great ❣️👍😍your channel
Anonymous
24 February 2024 at 16:15

Very nice questions
Loki
3 March 2024 at 05:54

Good
Anonymous
22 March 2024 at 08:30

Nice application 👍👍 9
Thank so much 🥰🥰
Very helpful for my pripresion
CeceliaO
13 July 2024 at 06:20

Very interesting information!Perfect just what I was looking for!Expand blog
Anonymous
17 July 2024 at 08:39

Super
Pinki Kumari
11 August 2024 at 06:09

If ccchjgcc

Related

7 thoughts on “Ratio & Proportion Questions”

Leave a Comment