71.A bag has coins of Rs. 1, 50 Paise and 25 Paise in ratio of 5 : 9 : 4. What is the worth of the bag if the total number of coins in the bag is 72?
एक बैग में 1 रुपये, 50 पैसे और 25 पैसे के सिक्के 5 : 9 : 4 के अनुपात में हैं। यदि बैग में सिक्कों की कुल संख्या 72 है, तो बैग में कुल कितने रूपये हैं?
Option”C” is correct
⇒ Number of Rs. 1 Coins = 5/18 × 72 = 20
⇒ Number of 50 Paise coins = 9/18 × 72 = 36
⇒ Number of 25 Paise coins = 4/18 × 72 = 16
⇒ Total worth of the bag = (20 × 1) + (0.5 × 36) + (0.25 × 16) = 20 + 18 + 4 = Rs. 42
72. The length of three pencils (A, B, and C) is in the ratio 2 : 3 : 4. If the length of B and C is increased by 4 cm and 8 cm respectively, the lengths of A and C will be in the ratio 2 : 5. Find the initial length of pencil B.
तीन पेंसिल (A, B और C) की लंबाई 2 : 3 : 4 के अनुपात में है। यदि B और C की लंबाई क्रमशः 4 सेमी और 8 सेमी बढ़ा दी जाती है, तो A और C की लंबाई 2 : 5 के अनुपात में होगी। पेंसिल B की प्रारंभिक लंबाई ज्ञात कीजिए।
Option”B” is correct
Let the length of three pencils A, B and C be 2x, 3x and 4x respectively.
2x / (4x + 8) = 2 / 5
x = 8.
The length of pencil B is 24.
73. In a company, there are 500 employees. After 200 more employees joined the company, ratio of male employees to female employees becomes 3 : 4. If certain number of female employees leave the company, then the ratio of male to the female employees in the company becomes equal. What is the number of female employees that leaves the company?
एक कंपनी में, 500 कर्मचारी हैं। और 200 कर्मचारियों के कंपनी में शामिल होने के बाद, पुरुष कर्मचारियों का महिला कर्मचारियों सेअनुपात 3: 4 हो जाता है। यदि कुछ महिला कर्मचारी कंपनी छोड़ देते है, तो कंपनी में पुरुष कर्मचारियों का महिला कर्मचारियों से अनुपात बराबर हो जाता है। कंपनी छोड़ने वाली महिला कर्मचारियों की संख्या कितनी है?
Option”D” is correct
Number of employees in the company = 500
New number of employees = 500 + 200 = 700
Let the number of male employees be 3x
Let the number of female employees be 4x
3x + 4x = 700
7x = 700
x = 100
Number of male employees in the company = 3x = 3 × 100 = 300
Number of female employees in the company = 4x = 4 × 100 = 400
Let y number of females leave the company then the ratio becomes 1 : 1
300/(400 – y) = 1/1
y = 100
100 employees left the company
74. In a mixture of 60 L, the ratio of milk and water is 2 : 3, then the quantity of water in the mixture is:
60 लीटर के मिश्रण में, दूध और पानी का अनुपात 2: 3 है, तो मिश्रण में पानी की मात्रा क्या है?
Option”C” is correct
Let the quantity of milk and water be 2x and 3x respectively
Total quantity of milk and water = 2x + 3x
⇒ 5x
According to question,
5x = 60
⇒ x = 12
Quantity of water = 3x
⇒ 3 × 12
⇒ 36 L
∴ The quantity of water in the mixture is 36 L
75. A sum of Rs. x was divided between A, B, C and D in the ratio 1/3 : 1/5 : 1/6 : 1/9. If the difference between the shares of B and D is Rs. 832, then the value of x is:
x रु. को A, B, C और D के बीच 1/3: 1/5: 1/6: 1/9 के अनुपात में विभाजित किया जाता है। यदि B और D के हिस्सो बीच का अंतर 832 रु है., तो x का मान है:
Option”A” is correct
Ratio of sum of A, B, C and D = 1/3 : 1/5 : 1/6 : 1/9 = 90/3 : 90/5 : 90/6 : 90/9 = 30 : 18 : 15 : 10
According to the question
⇒ 18 – 10 = 8 unit
⇒ 8 unit = 832
⇒ 1 unit = 104
⇒ Total sum = 30 + 18 + 15 + 10 = 73 unit
⇒ 73 unit = 104 × 73 = 7592
So, total sum is 7592.
76. A sum of Rs 5200 is divided amongst A, B, C, and D such that the ratio of shares of A and B is 2 : 3, that of B and C is 4 : 5 and that of C and D is 1 : 2. What is the difference between the shares of B and D?
5200 रुपए को A, B C और D के बीच इस प्रकार बांटा जाता है कि A और B के हिस्सों का अनुपात 2 : 3 है तथा B और C के हिस्सों का अनुपात 4 : 5 है और C और D के हिस्सों का अनुपात का 1 : 2 है, तो B और D के हिस्सों के बीच अंतर क्या है?
Option”A” is correct
Given:
The total sum of money = Rs. 5200
The ratio of the share of A and B = 2 ∶ 3
The ratio of the share of B and C = 4 ∶ 5
The ratio of the share of C and D = 1 ∶ 2
Calculations:
Simplifying the ratios to get the same unit by cross multiplication
Ratio of A and B = (2 ∶ 3) × 4
⇒ 8 ∶ 12
Ratio of B and C = (4 ∶ 5) × 3
⇒ 12 ∶ 15
Ratio of C and D = (1 ∶ 2) × 15
⇒ 15 ∶ 30
Ratio of A, B, C and D = 8 ∶ 12 ∶ 15 ∶ 30
Total sum = 8x + 12x + 15x + 30x
⇒ 65x = 5200
⇒ x = 80
Difference between the shares of B and D = 30x – 12x
⇒ 18 × 80
⇒ Rs. 1440
∴ The difference between the shares of B and D is Rs. 1440
77. In a bag, there are coins of 5ps, 10ps, and 25ps in a ratio of 3 : 2 : 1. If there are Rs. 60 in all, how many 5ps coins are there?
एक थैले में 5 पैसे, 10 पैसे और 25 पैसे के सिक्के 3 : 2 : 1 के अनुपात में हैं। यदि कुल मिलाकर इसमें 60 रुपये हैं, तो उसमें 5 पैसे के कितने सिक्के हैं?
Option”C” is correct
Given:
5p : 10p : 25p = 3 : 2 : 1 = 3x : 2x : x
Concept:
1 Rupee = 100 paise
Calculation:
60 Rupees = 60 × 100 = 6000 paise
⇒ 5 × 3x + 10 × 2x + 25 × 1x = 6000
⇒ 15x + 20x + 25x = 6000
⇒ 60x = 6000
⇒ x = 100
∴ Number of 5 paise coins = 3x = 3 × 100 = 300
78. If x : y = 6 : 5 and z : y = 9 : 25, then what is the ratio of x : z?
यदि x : y = 6 : 5 और z : y = 9 : 25 है, तो x : z का अनुपात क्या है?
Option”C” is correct
x : y = 6 : 5
And z : y = 9 : 25
Calculation :
x/y = 6/5 —- (i)
And z/y = 9/25
⇒ y/z = 25/9 —- (ii)
Multiply equation (i) and (ii) we get,
(x/y) × (y/z) = (6/5) × (25/9)
⇒ x/z = 10/3
∴ x : z = 10 : 3
Alternate Method
x : y = 6 : 5 —– (i)
And z : y = 9 : 25 —- (ii)
As y is in both the ratios, Multiply (i) × 5 to make equal value of y in both the ratios
x : y = (6 : 5) × 5 = 30 : 25 —- (iii)
from (ii) and (iii), Since y is same in both the ratios
x : z = 30 : 9 = 10 : 3
79. The ratio of number of children, women and men in colony is 6 : 4 : 3 respectively and the colony has at least 200 members. What will be minimum number of children in the colony?
एक कॉलोनी में बच्चों, महिलाओं और पुरुषों की संख्या का अनुपात क्रमशः 6 : 4 : 3 है और कॉलोनी में कम से कम 200 सदस्य हैं। कॉलोनी में बच्चों की न्यूनतम संख्या क्या होगी?
Option”D” is correct
The ratio of the number of children, women, and men in a colony is 6: 4: 3 respectively.
The colony has at least 200 members
CALCULATION:
Ratio = 6 : 4 : 3
Let children, women, and men be 6x, 4x, and 3x respectively.
Total member = 13x
So, members should be multiple of 13.
∴ We have to find the least multiple of 13 greater than 200. (∵ minimum number of children in the colony is asked)
As 13 × 16 = 208 there are a total of 208 members
⇒ 13x = 208 or x = 16
⇒ minimum number of Children = 6 × 16 = 96
∴ 96 will be minimum number of children in the colony.
80. There are two types of flowers in the garden. The ratio of the number of type A and type B flowers is 4 ∶ 5 And type B flowers are 15 more than type A then how many flowers are there in the garden?
बगीचे में दो प्रकार के फूल हैं। A प्रकार के और B प्रकार के फूलों की संख्या का अनुपात 4 ∶ 5 है और B प्रकार के फूल A से 15 अधिक है, तो बगीचे में कितने फूल हैं?
Option”C” is correct
Ratio of no. of type A and type B flowers is 4 ∶ 5
Type B flowers are 15 more than type A.
Explanation:
Let the no. of type A and type B flowers be 4x And 5x respectively.
According to question,
⇒ (No. of type B flowers) – (No. of type A flowers) = 15
Alternate Method
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