This set of Class 8 Maths Chapter 2 Multiple Choice Questions & Answers (MCQs) focuses on “Reduce the Linear Equation and Find the Value of the Variable”.
1. Solve: \(\frac{2x-11}{2} + \frac{x}{7}\) = 5.
a) x = \(\frac{147}{16}\)
b) x = \(\frac{16}{147}\)
c) x = \(\frac{14}{167}\)
d) x = \(\frac{167}{14}\)
View Answer
Explanation: \(\frac{2x-11}{2} + \frac{x}{7}\) = 5
∴\(\frac{7*(2x-11)}{7*2} + \frac{2*x}{2*7}\) = 5
∴\(\frac{14x-77+2x}{14}\) = 5
∴16x – 77 = 5 * 14
∴16x – 77 = 70
∴16x = 147
∴x = \(\frac{147}{16}\).
2. Solve: \(\frac{x}{5} + \frac{x}{7} = \frac{1}{35}\).
a) \(\frac{1}{6}\)
b) \(\frac{1}{8}\)
c) \(\frac{1}{12}\)
d) \(\frac{1}{10}\)
View Answer
Explanation: \(\frac{x}{5} + \frac{x}{7} = \frac{1}{35}\)
∴\(\frac{7*x+5*x}{5*7} = \frac{1}{35}\)
∴\(\frac{7x + 5x}{35} = \frac{1}{35}\)
∴\(\frac{12x}{35} = \frac{1}{35}\)
∴12x = 1
∴x = \(\frac{1}{12}\).
3. Solve: 3(x + 3) = 5(x + 2).
a) \(\frac{-1}{2}\)
b) \(\frac{1}{2}\)
c) 2
d) -2
View Answer
Explanation: 3(x + 3) = 5(x + 2)
∴ 3x + 9 = 5x + 10
∴ 3x – 5x = 10 – 9
∴ -2x = 1
∴ x = \(\frac{-1}{2}\).
4. Solve: \(\frac{m-2}{2} + \frac{2m+5}{3}\) = 2.
a) \(\frac{8}{7}\)
b) \(\frac{7}{8}\)
c) 8
d) 7
View Answer
Explanation:
\(\frac{m-2}{2} + \frac{2m+5}{3}\) = 2
∴ \(\frac{3*(m-2)}{3*2} + \frac{2*(2m+5)}{2*3}\) = 2
∴ \(\frac{3m-6+4m+10}{6}\) = 2
∴ \(\frac{7m+4}{6}\) = 2
∴ 7m + 4 = 12
∴ 7m = 8
∴ m = \(\frac{8}{7}\).
5. Solve: 12x – 3 = 9.
a) 1
b) -1
c) 12
d) -12
View Answer
Explanation: 12x – 3 = 9
∴12x = 12
∴x = 1.
6. Solve: \(\frac{2v-3}{2} + \frac{3v}{4}\) = 12.
a) \(\frac{14}{108}\)
b) \(\frac{108}{14}\)
c) \(\frac{54}{7}\)
d) \(\frac{7}{54}\)
View Answer
Explanation: \(\frac{2v-3}{2} + \frac{3v}{4}\) = 12
∴\(\frac{4*(2v-3)}{4*2} + \frac{2*3v}{4*2}\) = 12
∴\(\frac{8v-12+6v}{8}\) = 12
∴8v – 12 + 6v = 12 * 8
∴14v – 12 = 96
∴14v = 108
∴v = \(\frac{108}{14} = \frac{54}{7}\).
7. Solve: 0.25(12t – 4) = 1.
a) \(\frac{2}{3}\)
b) \(\frac{3}{2}\)
c) \(\frac{12}{11}\)
d) \(\frac{11}{12}\)
View Answer
Explanation: 0.25(12t – 4) = 1
∴3t – 1 = 1
∴3t = 2
∴t = \(\frac{2}{3}\).
8. Solve: 2y – 2 = 7y + 1.
a) \(\frac{-3}{5}\)
b) \(\frac{-5}{3}\)
c) \(\frac{2}{3}\)
d) \(\frac{3}{2}\)
View Answer
Explanation: 2y – 2 = 7y + 1
∴2y – 7y = 1 + 2
∴-5y = 3
∴y = \(\frac{-3}{5}\).
9. Solve: 3n – 13 = 13n + 31.
a) \(\frac{22}{5}\)
b) \(\frac{-22}{5}\)
c) \(\frac{-44}{10}\)
d) \(\frac{44}{10}\)
View Answer
Explanation: 3n – 13 = 13n + 31
∴3n – 13n = 31 + 13
∴-10n = 44
∴n = \(\frac{-44}{10} = \frac{-22}{5}\).
10. Solve: 2x – 3 = 0.
a) \(\frac{3}{2}\)
b) \(\frac{2}{3}\)
c) \(\frac{3}{5}\)
d) \(\frac{5}{3}\)
View Answer
Explanation: 2x – 3 = 0
∴2x = 3
∴x = \(\frac{3}{2}\).
11. Solve: \(\frac{14y-12}{12y-14} = \frac{1}{2}\)
a) \(\frac{10}{16}\)
b) \(\frac{8}{5}\)
c) \(\frac{5}{8}\)
d) \(\frac{16}{10}\)
View Answer
Explanation: \(\frac{14y-12}{12y-14} = \frac{1}{2}\)
∴2 * (14y – 12) = 1 * (12y – 14)
∴28y – 24 = 12y – 14
∴28y – 12y = -14 + 24
∴16y = 10
∴y = \(\frac{10}{16} = \frac{5}{8}\).
Sanfoundry Global Education & Learning Series – Mathematics – Class 8.
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