Author name: Umar

Correct Answer: 5 days

Work problems are based on the principle that the amount of work remains constant. Total work can be calculated by multiplying the number of workers by the number of days. Here, 5 men × 6 days = 30 man-days. If the same work is to be completed by 6 men, the required time is 30 ÷ 6 = 5 days. This demonstrates an inverse relationship between the number of workers and the time taken to complete a fixed amount of work. As the number of workers increases, the number of days decreases proportionally, assuming every worker performs at the same rate and works for the same duration each day.

• Total Work: 5 × 6 = 30 man-days.
• Required Workers: 6 men.
• Time Required: 30 ÷ 6 = 5 days.
• Concept: Inverse Proportion.
• Correct Answer: 5 days.

Correct Answer: 7

To evaluate the expression 16/4 + 9 − 6, we apply the order of operations (BODMAS/PEMDAS). Division is performed before addition and subtraction. First, divide 16 by 4 to obtain 4. The expression then becomes 4 + 9 − 6. Next, perform addition: 4 + 9 = 13. Finally, subtract 6 from 13 to get 7. Following the correct order of operations ensures accurate results in arithmetic calculations. Questions of this type are commonly asked in competitive examinations to test understanding of mathematical rules and calculation speed.

• Step 1: 16 ÷ 4 = 4.
• Step 2: 4 + 9 = 13.
• Step 3: 13 − 6 = 7.
• Rule Used: BODMAS (Order of Operations).
• Correct Answer: 7.

The correct answer is 5. A ratio expresses the proportional relationship between parts of a whole. In the given ratio 1 : x : 5, the three parts are represented by 1, x, and 5 respectively. Since the problem states that their total sum equals 11, we can directly translate this into a simple algebraic equation.

Solving the Equation Step by Step

• Form the equation: The sum of the ratio parts is 1 + x + 5. We set this equal to 11:
  • 1 + x + 5 = 11
• Combine the known numbers: Add 1 and 5 to get 6. The equation simplifies to:
  • x + 6 = 11
• Isolate the variable: Subtract 6 from both sides of the equation to solve for x:
  • x = 11 − 6
  • x = 5

Thus, the missing term in the ratio is 5, making the complete ratio 1 : 5 : 5. A quick verification confirms our solution: 1 + 5 + 5 = 11, which perfectly matches the given sum.

Why the Other Options Are Incorrect

• Option 2 (6): If x = 6, the sum would be 1 + 6 + 5 = 12, which is greater than 11.
• Option 3 (7): If x = 7, the sum would be 1 + 7 + 5 = 13, which does not match.
• Option 4 (8): If x = 8, the sum would be 1 + 8 + 5 = 14, again incorrect.

Hence, the only value that satisfies the condition is x = 5, which corresponds to Option 1.