Question : The sum of three numbers is 2, the 1st number is $\frac{1}{2}$ times the 2nd number and the 3rd number is $\frac{1}{4}$ times the 2nd number. The 2nd number is:
Option 1: $\frac{7}{6}$
Option 2: $\frac{8}{7}$
Option 3: $\frac{9}{8}$
Option 4: $\frac{10}{9}$
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Correct Answer: $\frac{8}{7}$
Solution : Let the second number be $x$, the first number be $ \frac{x}{2}$ and the third number be $\frac{x}{4}$. According to the question, ⇒ $\frac{x}{2}+x+\frac{x}{4}=2$ ⇒ $\frac{2x+4x+x}{4} =2$ ⇒ $2x+4x+x=8$ ⇒ $7x=8$ $\therefore x=\frac{8}{7}$ Hence, the correct answer is $\frac{8}{7}$.
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Question : Directions: By interchanging the given two signs and numbers which of the following equations will be correct? × and +, 9 and 6
Option 1: 7 × 6 ÷ 3 + 9 – 8 = 17
Option 2: 6 × 8 – 9 ÷ 3 + 5 = 50
Option 3: 7 + 6 × 4 ÷ 9 – 8 = 8
Option 4: 9 × 7 + 4 ÷ 1 – 6 = 7
Question : The sum of the first 20 term of the series $\frac{1}{5×6}+\frac{1}{6×7}+\frac{1}{7×8}+....$ is:
Option 1: 0.16
Option 2: 1.6
Option 3: 16
Option 4: 0.016
Question : Directions: By Interchanging the given two numbers which of the following equations will be not correct? 7 and 9
Option 1: 8 × 3 ÷ 6 + 9 – 7 = 2
Option 2: 7 + 6 – 9 × 4 ÷ 2 = 2
Option 3: 9 + 4 × 3 – 7 ÷ 1 = 10
Option 4: 9 × 3 + 4 ÷ 2 – 7 = 14
Question : Directions: By Interchanging the given two numbers which of the following equations will be not correct? 7 and 4
Option 1: 8 ÷ 6 × 9 + 7 – 4 = 12
Option 2: 7 × 8 + 4 – 6 ÷ 3 = 37
Option 3: 9 – 4 × 3 + 6 × 7 ÷ 1 = 12
Option 4: 4 × 8 – 9 ÷ 3 + 7 = 57
Question : The value of $4 \div 12$ of $[3 \div 4$ of $\{(4-2) \times 6 \div 2\}]-2 \times 6 \div 8+3$ is:
Option 1: $4 \frac{1}{6}$
Option 2: $3 \frac{1}{3}$
Option 3: $2 \frac{1}{3}$
Option 4: $7 \frac{1}{6}$
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