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।
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-
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।
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।
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.
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 –
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?
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:
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।
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 5l2+m2+n2l2−−−−−−−−√5l2+m2+n2l2 is equal to:
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