11. If x + y + z = 400 and x : y : z = 1 : 1 : 2, then what is the value of z?
यदि x + y + z = 400 और x : y : z = 1 : 1 : 2 है, तो z का मान क्या है?
Option”B” is correct
Let the value of x, y and z be a, a, and 2a
⇒ x + y + z = 400 [Given]
⇒ a + a + 2a = 400
⇒ a = 100
⇒ The value of z = 2a = 200
∴ The value of z is 200.
12.The sum of two numbers x and y is 48 and their difference is 6. Then x : y = ?
दो संख्याओं x और y का योग 48 है और उनका अंतर 6 है, तो x : y = ?
Option”D” is correct
Given, x + y = 48 …1)
⇒ x – y = 6 …2)
From (1) + (2)
⇒ x = 27
⇒ y = 21
⇒ x : y = 27 : 21 = 9 : 7
∴ The ratio of x : y is 9 : 7
13. The monthly incomes of A and B are in the ratio 3 : 4 and the ratio of their monthly expenditures is 2 : 3. If each saves Rs. 4000 per month, then what is the income of B?
A और B की मासिक आय का अनुपात 3 : 4 है और उनके मासिक व्यय का अनुपात 2 : 3 है। यदि प्रत्येक प्रति माह 4000 रूपए की बचत करता है, तब B की आय क्या है?
Option”C” is correct
Let the monthly income of A and B be 3x and 4x
And the monthly expenditures be 2y and 3y
Saving = income – expenditure
4000 = 4x – 3y …1)
Similarly,
4000 = 3x – 2y …2)
From 2 × (1) – 3 × (2)
8000 – 12000 = 8x – 9x
x = 4000
The income of B = 4x = 16000
∴ The income of B is 16000.
14. If (A + B): (B + C): (C + A) = 6: 7: 5, then find the value of C: (A + B)?
यदि (A + B): (B + C): (C + A) = 6: 7: 5, तो C: (A + B) का मान ज्ञात कीजिए?
Option”A” is correct
Let,
(A + B) = 6x —- (1)
(B + C) = 7x —- (2)
(C + A) = 5x —- (3)
Adding equations (1), (2) and (3),we get
2(A + B + C) = 6x + 7x + 5x
A + B + C = 9x —- (4)
From equations (1) and (4):
C = 3x
From equations (2) and (4):
A = 2x
From equations (3) and (4):
B = 4x
Now, C: (A + B) = 3x : 6x = 1 : 2
15. The sum of the squares of 3 natural numbers is 1029, and they are in the proportion 1 : 2 : 4, The difference between the greatest number and the smallest number is:
3 प्राकृतिक संख्याओं के वर्गों का योग 1029 है, और वे 1 : 2 : 4 के अनुपात में हैं, सबसे बड़ी संख्या और सबसे छोटी संख्या के बीच का अंतर ज्ञात कीजिये।
Option”D” is correct
The ratio of three natural numbers = x : 2x : 4x
According to the question
x2 + (2x)2 + (4x)2 = 1029
⇒ x2 + 4x2 + 16x2 = 1029
⇒ 21x2 = 1029
⇒ x2 = 1029/21
⇒ x2 = 49
⇒ x = √49 = 7
∴ Difference between greatest number and smallest numbers = 4x – x = 3x = 3 × 7 = 21
16. The ratio of the number of boys and girls in a school is 3 : 2. If 20% of the boys and 25% of the girls are scholarship holders, the percentage of the school students who are not scholarship holders is:
एक स्कूल में लड़कों और लड़कियों की संख्या का अनुपात 3 : 2 है। यदि 20% लड़के और 25% लड़कियां छात्रवृत्ति प्राप्त करती हैं, तो स्कूल में छात्रवृत्ति नहीं प्राप्त करने वाले छात्रों की संख्या का प्रतिशत है:
Option”B” is correct
Ratio of the number of boys and girls in a school is = 3 : 2 or 30 : 20
Let number of boys = 30 and number of girls = 20
Total students = 30 + 20 = 50
Number of boys who did not get scholarship = 30 × (80/100) = 24
Number of girls who did not get scholarship = 20 × (75/100) = 15
Total number of students who did not get scholarship = 24 + 15 = 39
∴ Percentage of students who did not get scholarship = 39/50 × 100 = 78%
17. If three numbers are in the ratio 2 : 3 : 5 and the twice of their sum is 200. The square of the largest of three numbers is:
यदि तीन संख्याएँ 2: 3: 5 के अनुपात में हैं और उनके योग का दोगुना 200 है। तीन संख्याओं में से सबसे बड़ी संख्या का वर्ग क्या है?
Option”D” is correct
Given:
Ratio of three numbers is 2 : 3 : 5
Twice of their sum is 200
Calculation:
⇒ 2 + 3 + 5 = 10 unit
According to the question,
⇒ 10 unit = 200/2
⇒ 1 unit = 10
⇒ 5 unit = 50
The square of the largest of three numbers is 2500.
18. If 25 percent of a number is subtracted from itself then the ratio of the number obtained to the other number is 2 : 1. Find the ratio between the first numbers to the second number.
यदि किसी संख्या के 25 प्रतिशत को स्वयं उस संख्या से घटाया जाता है, तो प्राप्त संख्या और दूसरी संख्या का अनुपात 2 : 1 है। पहली संख्या और दूसरी संख्या के बीच अनुपात ज्ञात कीजिए।
Option”D” is correct
Let the 1st and 2nd numbers be A and B respectively
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