Quantitative Aptitude

Simple Equations: Practice Questions with Answers

14 practice questions on Simple Equations, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.

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1. Q.1

   3 pens and 2 pencils cost ₹78. 5 pens and 3 pencils cost ₹128. Find the cost of one pen and one pencil.

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   Answer: Pen = ₹22, Pencil = ₹6

   Solution:

   1. Let a pen cost p and a pencil cost q: 3p + 2q = 78 … (1), and 5p + 3q = 128 … (2).
   2. Scale to eliminate q: multiply (1) by 3 and (2) by 2: 9p + 6q = 234, and 10p + 6q = 256.
   3. Subtract: p = 256 − 234 = 22. Substitute into (1): 3(22) + 2q = 78 → 66 + 2q = 78 → q = 6.
   4. Check in (2): 5(22) + 3(6) = 110 + 18 = 128. Matches.

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2. Q.2

   Five years ago, a father was three times as old as his son. Ten years from now, the father will be twice as old as the son. Find their present ages.

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   Answer: Father: 50 years, Son: 20 years

   Solution:

   1. Let the son’s present age = s and the father’s present age = f.
   2. Five years ago: f − 5 = 3(s − 5), so f = 3s − 10.
   3. Ten years from now: f + 10 = 2(s + 10), so f = 2s + 10.
   4. Setting these equal: 3s − 10 = 2s + 10, so s = 20, and f = 2(20) + 10 = 50.

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3. Q.3

   A number is 8 more than twice another number. If the sum of the two numbers is 50, find both numbers.

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   Answer: 36 and 14

   Solution:

   1. Let the numbers be x and y, with x = 2y + 8.
   2. Substituting into x + y = 50: (2y + 8) + y = 50, so 3y = 42, giving y = 14.
   3. Then x = 2(14) + 8 = 36.

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4. Q.4

   If 3 is added to both the numerator and denominator of a fraction, it becomes 3/4. If 1 is subtracted from both, it becomes 1/2. Find the original fraction.

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   Answer: 3/5

   Solution:

   1. Let the fraction be x/y. (x+3)/(y+3) = 3/4 → 4x + 12 = 3y + 9 → 4x − 3y = −3 … (1).
   2. (x−1)/(y−1) = 1/2 → 2x − 2 = y − 1 → y = 2x − 1 … (2).
   3. Substitute (2) into (1): 4x − 3(2x−1) = −3 → 4x − 6x + 3 = −3 → −2x = −6 → x = 3. Then y = 2(3) − 1 = 5.
   4. Check: (3+3)/(5+3) = 6/8 = 3/4. (3−1)/(5−1) = 2/4 = 1/2. Both match.

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5. Q.5

   The sum of two numbers is 45, and their difference is 11. Find the two numbers.

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   Answer: 28 and 17

   Solution:

   1. Let the numbers be x and y: x + y = 45 and x − y = 11.
   2. Adding the two equations: 2x = 56, so x = 28.
   3. Substituting back: y = 45 − 28 = 17.

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6. Q.6

   Three times a number, decreased by 7, equals twice the number increased by 9. Find the number.

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   Answer: 16

   Solution:

   1. Let the number be x: 3x − 7 = 2x + 9.
   2. Subtracting 2x from both sides: x − 7 = 9, so x = 16.

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7. Q.7

   The sum of three consecutive integers is 72. Find the integers.

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   Answer: 23, 24, 25

   Solution:

   1. Let the integers be x, x+1, x+2. Their sum: x + (x+1) + (x+2) = 72 → 3x + 3 = 72 → x = 23.
   2. The integers are 23, 24, 25.

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8. Q.8

   If 2 is added to both the numerator and denominator of a fraction, it becomes 1/2. If 1 is subtracted from both, it becomes 1/3. Find the original fraction.

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   Answer: 4/10 (= 2/5). Solve y=2x+2 and y=3x-2 together to get x=4, y=10.

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9. Q.9

   Four times a number, decreased by 9, equals the number increased by 21. Find the number.

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   Answer: 10

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10. Q.10

    The sum of four consecutive integers is 94. Find the largest of the four.

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    Answer: 25. 4x+6=94 gives x=22; largest is x+3.

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11. Q.11

    The sum of two numbers is 60, and their difference is 14. Find the two numbers.

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    Answer: 37 and 23

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12. Q.12

    A number is 5 more than three times another number. If the sum of the two numbers is 45, find both numbers.

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    Answer: 35 and 10

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13. Q.13

    4 notebooks and 3 pens cost ₹84. 3 notebooks and 2 pens cost ₹59. Find the cost of one notebook and one pen.

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    Answer: Notebook = ₹9, Pen = ₹16. Eliminate using 2×(first) and 3×(second).

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14. Q.14

    The sum of three consecutive even numbers is 72. Find the numbers.

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    Answer: 22, 24, 26. x+(x+2)+(x+4)=72 gives x=22.

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