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Free Linear Equations MCQs with Answers

78 Linear Equations MCQs from Mathematics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.

Linear equations contain variables only to the first power and produce straight-line relationships when represented graphically. Problems involve solving equations with brackets, fractions, and variables on both sides, forming equations from statements, and handling simultaneous linear equations, which differ from quadratic equations by having no squared variable.

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78 questions · page 2 of 4

21. A bag contains a total of 93 coins in the form of one rupee and 50 paise coins. If the total value of coins in the bag is Rs.56, find the number of 50 paise coins in the bag?

  • A. 60
  • B. 56
  • C. 64
  • D. 74
  • E. None of these

Explanation: If there are x 50-paisa coins, there are 93 - x one-rupee coins. Their value is Rs.0.50x + Rs.1(93 - x) = Rs.56, so 93 - 0.50x = 56 and x…

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Correct answer: 74

22. The cost of 16 pens and 8 pencils is Rs.352 and the cost of 4 pens and 4 pencils is Rs.96. Find the cost of each pen?

  • A. Rs.32
  • B. Rs.28
  • C. Rs.36
  • D. Rs.25
  • E. None of these

Explanation: Let a pen cost p rupees and a pencil cost c rupees. Dividing 16p + 8c = Rs.352 by 8 gives 2p + c = Rs.44, while 4p + 4c = Rs.96 gives p +…

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Correct answer: None of these

23. the present average age of a couple and their daughter is 35 years. Fifteen years from now, the age of the mother will be equal to the sum of present ages of the father and the daughter. Find the present age of mother?

  • A. 43 years
  • B. 40 years
  • C. 48 years
  • D. 45 years
  • E. None of these

Explanation: The present total age is 3 x 35 years = 105 years. If the mother's age is M years, the condition 15 years from now gives M + 15 = 105 - M…

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Correct answer: 45 years

24. Ten years ago, the age of Aftab was one-third the age of Kashif at that time. The present age of Kashif is 12 years more than the present age of Aftab. Find the present age of Aftab?

  • A. 14
  • B. 16
  • C. 18
  • D. 20
  • E. None of these

Explanation: Let Aftab's present age be A years, so Kashif's present age is A + 12 years.

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Correct answer: 16

25. Masood's age 18 years hence will be thrice his age four years ago. Find Masood's present age?

  • A. 12 years
  • B. 21 years
  • C. 18 years
  • D. 9 years
  • E. None of these

Explanation: Let Masood's present age be M years. The condition gives M + 18 = 3(M - 4), so M + 18 = 3M - 12, 2M = 30 and M = 15 years.

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Correct answer: None of these

26. When 2 is added to half of one-third of one-fifth of a number, the result is one-fifteenth of the number. Find the number?

  • A. 40
  • B. 50
  • C. 60
  • D. 70
  • E. None of these

Explanation: Half of one-third of one-fifth of n is n/30. Therefore 2 + n/30 = n/15; multiplying by 30 gives 60 + n = 2n, so n = 60.

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Correct answer: 60

27. In a three digit number, the hundred digit is 2 more than the tens digit and the units digit is 2 less than the tens digit. If the sum of the digits is 18, find the number?

  • A. 975
  • B. 753
  • C. 642
  • D. 684
  • E. None of these

Explanation: Let the tens digit be t, so the hundreds digit is t + 2 and the units digit is t - 2.

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Correct answer: None of these

28. The number obtained by interchanging the two digits of a two-digit number is less than the original number by 45. If the sum of the two digits of the number so obtained is 13, then what is the original number?

  • A. 49
  • B. 94
  • C. 83
  • D. Either (a) or (b)
  • E. None of these

Explanation: Let the original number be 10a + b and its reversal 10b + a. Since the reversal is 45 less, 9(a - b) = 45, so a - b = 5; with a + b = 13…

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Correct answer: 94

29. The sum of the digits of a two-digit number is 12. The difference of the digits is 6. Find the number?

  • A. 93
  • B. 39
  • C. 75
  • D. 48
  • E. Either (a) or (b)

Explanation: Let the digits be a and b. Then a + b = 12 and their absolute difference is 6, giving the digit pair 9 and 3; because the order is not…

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Correct answer: Either (a) or (b)

30. The tens digit of a two-digit number is two more than its unit digit. The two-digit number is 7 times the sum of the digits. Find the units digits?

  • A. 1
  • B. 2
  • C. 3
  • D. 4
  • E. None of these

Explanation: Let the units digit be u, so the tens digit is u + 2. The number is 10(u + 2) + u = 11u + 20, while seven times the digit sum is 7(2u + 2)…

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Correct answer: 2

31. Solve the equation for x : 6x - 27 + 3x = 4 + 9 - x

  • A. 4
  • B. 5
  • C. 6
  • D. -4
  • E. None of these

Explanation: Combine like terms: 6x + 3x - 27 = 4 + 9 - x gives 9x - 27 = 13 - x, so 10x = 40 and x = 4.

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Correct answer: 4

32. Solve the equation for x : 19(x + y) + 17 = 19(-x + y) - 21

  • A. -1
  • B. -2
  • C. -3
  • D. -4
  • E. None of these

Explanation: Expand both sides: 19x + 19y + 17 = -19x + 19y - 21; the y terms cancel, giving 38x = -38 and x = -1.

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Correct answer: -1

33. The cost of 2 chairs and 3 tables is Rs.1300. The cost of 3 chairs and 2 tables is Rs.1200. The cost of each table is more than that of each chair by__________?

  • A. Rs.70
  • B. Rs.75
  • C. Rs.50
  • D. Rs.60
  • E. None of these

Explanation: Let a chair cost c rupees and a table cost t rupees. From 2c + 3t = 1300 and 3c + 2t = 1200, solving gives t = 300 rupees and c = 200…

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Correct answer: None of these

34. The denominator of a fraction is 1 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 3/5. Find the fraction?

  • A. 2/3
  • B. 3/5
  • C. 4/7
  • D. 5/9
  • E. None of these

Explanation: Let the numerator be n, so the denominator is 2n - 1. After increasing both by 1, (n + 1)/(2n) = 3/5, giving 5n + 5 = 6n, n = 5 and…

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Correct answer: 5/9

35. A person ordered 5 pairs of black socks and some pairs of brown socks. The price of a black pair was thrice that of a brown pair while preparing the bill the bill clerk inter-changed the number of black and brown pairs by mistake which increased the bill by 100% what was the number of pair of brown socks in the original order?

  • A. 10
  • B. 15
  • C. 20
  • D. 25

Explanation: Let the price of one brown pair be p and let the number of brown pairs be n, so one black pair costs 3p.

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Correct answer: 25

36. 3648.24 + 364.824 / ? - 36.4824 = 3794.1696

  • A. 2
  • B. 3
  • C. 4
  • D. 5

Explanation: First isolate the unknown term: 3648.24 + 364.824 / ? - 36.4824 = 3794.1696, so 364.824 / ? = 182.412. Since 182.412 x 2 = 364.824, ?

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Correct answer: 2

37. 24 - [2.4 - {0.24 * 2 - (0.024 - ?)}] = 22.0584

  • A. 0.0024
  • B. 0.024
  • C. 0.24
  • D. 0.00024

Explanation: Let the missing value be x. Inside the braces, 0.24 x 2 - (0.024 - x) = 0.456 + x, so the whole expression becomes 24 - (1.944 - x) =…

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Correct answer: 0.0024

38. 21345 * 45 = 4270 * ?

  • A. 215
  • B. 235
  • C. 225
  • D. 255

Explanation: Let the unknown be x and rearrange: x = (21345 x 45) / 4270. Since 21345 / 4270 is approximately 4.9988, x is approximately 4.9988 x 45 =…

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Correct answer: 225

39. 25 * 25 / 25 + 15 * 40 = ________?

  • A. 125
  • B. 525
  • C. 25/64
  • D. 625Standardized & Admissions Tests

Explanation: Multiplication and division are performed before addition: 25 x 25 / 25 = 25, and 15 x 40 = 600.

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Correct answer: 625Standardized & Admissions Tests

40. {20 - [7 - (3 -2)] + 1/3 (4.2)} / 1.4 = ________?

  • A. 11
  • B. 12
  • C. 14
  • D. 19

Explanation: First, 3 - 2 = 1, so [7 - (3 - 2)] = 6. Also, 1/3 x 4.2 = 1.4, giving {20 - 6 + 1.4} / 1.4 = 15.4 / 1.4 = 11; option b commonly results…

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Correct answer: 11
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