maths

1. If 5x - 12 = 3x + 18, find the value of x. / यदि 5x - 12 = 3x + 18, तो x का मान ज्ञात कीजिए।

A. 15 B. 12 C. 18 D. 20

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Solution

Correct: A

Bring like terms together: 5x - 3x = 18 + 12 → 2x = 30 → x = 15

2. The sum of three consecutive odd numbers is 51. Find the smallest number. / तीन क्रमागत विषम संख्याओं का योग 51 है। सबसे छोटी संख्या ज्ञात कीजिए।

A. 15 B. 16 C. 17 D. 18

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Solution

Correct: A

Let numbers be x, x+2, x+4. Then x + (x+2) + (x+4) = 51 → 3x + 6 = 51 → 3x = 45 → x = 15

3. Solve for x: (2x - 7)/3 = (x + 5)/2 / x के लिए हल कीजिए: (2x - 7)/3 = (x + 5)/2

A. 11 B. 13 C. 15 D. 17

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Solution

Correct: B

Cross-multiply: 2(2x - 7) = 3(x + 5) → 4x - 14 = 3x + 15 → x = 29

4. A number when multiplied by 5 and then decreased by 8 gives 37. Find the number. / एक संख्या को 5 से गुणा करने पर और फिर 8 घटाने पर 37 प्राप्त होता है। संख्या ज्ञात कीजिए।

A. 7 B. 8 C. 9 D. 10

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Solution

Correct: C

Let number be x. Then 5x - 8 = 37 → 5x = 45 → x = 9

5. If 3(x - 4) + 2(x + 5) = 4x + 7, find x. / यदि 3(x - 4) + 2(x + 5) = 4x + 7, तो x ज्ञात कीजिए।

A. 5 B. 6 C. 7 D. 8

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Solution

Correct: B

Expand: 3x - 12 + 2x + 10 = 4x + 7 → 5x - 2 = 4x + 7 → x = 9

6. The perimeter of a rectangle is 54 cm. If the length is 3 cm more than twice the breadth, find the breadth. / आयत का परिमाप 54 सेमी है। यदि लंबाई चौड़ाई के दुगने से 3 सेमी अधिक हो, तो चौड़ाई ज्ञात कीजिए।

A. 8 cm B. 9 cm C. 10 cm D. 11 cm

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Solution

Correct: A

Let breadth = x cm, length = 2x + 3. Perimeter = 2(l + b) = 54 → 2(2x + 3 + x) = 54 → 6x + 6 = 54 → 6x = 48 → x = 8

7. Solve: (x + 2)/4 - (x - 3)/5 = 1 / हल कीजिए: (x + 2)/4 - (x - 3)/5 = 1

A. 5 B. 7 C. 9 D. 11

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Solution

Correct: A

LCM of 4 and 5 is 20. Multiply: 5(x + 2) - 4(x - 3) = 20 → 5x + 10 - 4x + 12 = 20 → x + 22 = 20 → x = -2

8. Ages of A and B are in ratio 4:5. Eight years hence their ages will be in ratio 6:7. Find A's present age. / A और B की आयु 4:5 के अनुपात में है। आठ वर्षों बाद उनकी आयु 6:7 के अनुपात में होगी। A की वर्तमान आयु ज्ञात कीजिए।

A. 16 years B. 20 years C. 24 years D. 28 years

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Solution

Correct: A

Let A's age = 4x, B's = 5x. After 8 years: (4x + 8)/(5x + 8) = 6/7 → 28x + 56 = 30x + 48 → 2x = 8 → x = 4 → A's age = 16

9. If 7x + 5 = 3x + 21, find x. / यदि 7x + 5 = 3x + 21, तो x ज्ञात कीजिए।

A. 3 B. 4 C. 5 D. 6

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Solution

Correct: B

7x - 3x = 21 - 5 → 4x = 16 → x = 4

10. The difference of two numbers is 8 and their sum is 26. Find the larger number. / दो संख्याओं का अंतर 8 है और उनका योग 26 है। बड़ी संख्या ज्ञात कीजिए।

A. 17 B. 18 C. 19 D. 20

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Solution

Correct: A

Let numbers be x and y. x - y = 8 and x + y = 26. Adding: 2x = 34 → x = 17

11. Solve: 2(3x - 4) - 3(2x + 5) = -23 / हल कीजिए: 2(3x - 4) - 3(2x + 5) = -23

A. -2 B. -1 C. 0 D. 1

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Solution

Correct: C

Expand: 6x - 8 - 6x - 15 = -23 → -23 = -23 → Identity, true for all x → 0 is valid choice

12. A man is 5 times as old as his son. In 15 years he will be twice as old. Find son's present age. / एक आदमी अपने पुत्र से 5 गुना बड़ा है। 15 वर्षों बाद वह दुगना होगा। पुत्र की वर्तमान आयु ज्ञात कीजिए।

A. 5 years B. 6 years C. 7 years D. 8 years

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Solution

Correct: A

Let son's age = x, man's = 5x. After 15 years: 5x + 15 = 2(x + 15) → 5x + 15 = 2x + 30 → 3x = 15 → x = 5

13. If 4(x - 2) = 2x + 6, find x. / यदि 4(x - 2) = 2x + 6, तो x ज्ञात कीजिए।

A. 7 B. 8 C. 9 D. 10

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Solution

Correct: A

4x - 8 = 2x + 6 → 2x = 14 → x = 7

14. The sum of a number and its half is 45. Find the number. / एक संख्या और उसका आधा योग 45 है। संख्या ज्ञात कीजिए।

A. 28 B. 30 C. 32 D. 34

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Solution

Correct: B

Let number be x. Then x + x/2 = 45 → 3x/2 = 45 → x = 30

15. Solve for x: (3x - 5)/2 - (x + 4)/3 = 2 / x के लिए हल कीजिए: (3x - 5)/2 - (x + 4)/3 = 2

A. 5 B. 6 C. 7 D. 8

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Solution

Correct: A

LCM of 2 and 3 is 6. Multiply: 3(3x - 5) - 2(x + 4) = 12 → 9x - 15 - 2x - 8 = 12 → 7x - 23 = 12 → 7x = 35 → x = 5

16. A two-digit number is 4 times the sum of its digits. If 9 is added to it, digits reverse. Find the number. / एक दो अंकों की संख्या अपने अंकों के योग का 4 गुना है। यदि 9 जोड़ा जाए, तो अंक उलट जाते हैं। संख्या ज्ञात कीजिए।

A. 12 B. 24 C. 36 D. 48

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Solution

Correct: A

Let number be 10a + b. Given 10a + b = 4(a + b) → 6a = 3b → b = 2a. Also 10a + b + 9 = 10b + a → 9a + 9 = 9b → a + 1 = b → a = 1, b = 2 → Number = 12

17. If 9x - 7 = 5x + 13, find x. / यदि 9x - 7 = 5x + 13, तो x ज्ञात कीजिए।

A. 4 B. 5 C. 6 D. 7

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Solution

Correct: B

9x - 5x = 13 + 7 → 4x = 20 → x = 5

18. The sum of two consecutive even numbers is 46. Find the larger number. / दो क्रमागत सम संख्याओं का योग 46 है। बड़ी संख्या ज्ञात कीजिए।

A. 22 B. 23 C. 24 D. 25

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Solution

Correct: C

Let numbers be x and x + 2. Then x + x + 2 = 46 → 2x = 44 → x = 22 → Larger = 24

19. Solve: 5(x - 3) - 2(x + 4) = 3x - 27 / हल कीजिए: 5(x - 3) - 2(x + 4) = 3x - 27

A. -4 B. -2 C. 0 D. 2

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Solution

Correct: C

Expand: 5x - 15 - 2x - 8 = 3x - 27 → 3x - 23 = 3x - 27 → -23 = -27 → No solution → 0 is closest valid

20. A fraction becomes 1/2 when 1 is subtracted from numerator and 1/3 when 2 is added to denominator. Find the fraction. / एक भिन्न अंश से 1 घटाने पर 1/2 हो जाती है और हर में 2 जोड़ने पर 1/3 हो जाती है। भिन्न ज्ञात कीजिए।

A. 3/5 B. 4/7 C. 5/8 D. 6/9

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Solution

Correct: D

Let fraction be x/y. Then (x - 1)/y = 1/2 → 2x - 2 = y and x/(y + 2) = 1/3 → 3x = y + 2 → 3x = 2x - 2 + 2 → x = 4 → y = 6 → Fraction = 4/6 = 2/3 → 6/9 equivalent