Apptitude

Question 1

What is the formula for calculating the mirror image of a clock?

Answer 1

Answer:
- For a rounded clock, subtract the given time from 12:00.
- For a non-rounded clock, subtract the given time from 11:60.

Explanation:
To find the mirror image of a time shown on the clock:
1. Identify the given time.
2. Use the corresponding formula:
- For a standard 12-hour clock (rounded), subtract the time from 12:00.
- For a clock without round markings (non-rounded), subtract the time from 11:60 to account for hour-minute alignment.

Question 2

How to subtract a mixed fraction number from a whole number?

Answer 2

Answer:
1. Increase the whole number of the mixed fraction by 1 (add 1 to the whole number).
2. Subtract the numerator from the denominator in the fraction to form a new fraction. Keep the denominator unchanged.
3. Subtract the increased whole number of the mixed fraction from the original whole number.
4. Add the calculated fraction to the result.

Example:
Subtract 13 4/6 from 25.

1. Increase 13 by 1 → 14.
2. Subtract the numerator from the denominator → (6 - 4 = 2).
   
   • New fraction: 2/6.
3. Subtract the whole number (14) from (25) → (25 - 14 = 11).
4. Add the calculated fraction: 11 2/6.

Final Answer: 11 2/6.

Question 3

What is the formula for calculating the water image of a clock?

Answer 3

Answer:
1. If the minute value is below 30 minutes: Subtract the given time from 18.30.
2. If the minute value is 30 or above: Subtract the given time from 17.90.

Example 1 (Minutes below 30):
Find the water image of 3:15.
- Subtract 3:15 from 18:30:
( 18:30 - 3:15 = 15:15 ).
- The water image is 15:15.

Example 2 (Minutes above 30):
Find the water image of 8:45.
- Subtract 8:45 from 17:90:
( 17:90 - 8:45 = 9:45 ).
- The water image is 9:45.

Question 4

What is the formula for calculating the angle between the hour hand and minute hand of a clock?

Answer 4

Answer:
The formula to calculate the angle between the hour hand and the minute hand is:
(60H - 11M) / 2

Where:
H = Hours
M = Minutes

Example: Find the angle at 5:30

1. Substitute the values into the formula:
   • For the hour hand:
     60H = 60 x 5 = 300
   • For the minute hand:
     11M = 11 x 30 = 330
2. Find the absolute difference:
   (Subtract the minimum value from bigger value, no matter whether it is hour or minute)
   330 - 300 = 30
3. Divide the difference by 2 to get the angle:
   30 / 2 = 15°So, the inner angle between the hour and minute hands at 5:30 is 15°.
4. To find the outer angle:
   Subtract the inner angle from 360°:
   360° - 15° = 345°So, the outer angle is 345°.

Conclusion:
At 5:30, there are two possible angles:
- The inner angle = 15°
- The outer angle = 345°

This method can be applied to any time on the clock to calculate the angle between the hour hand and minute hand.

Question 5

How to calculate the angle between the minute hand and hour hand with the mixed fraction value in the minute value?

Answer 5

Answer:
To calculate the angle between the hour hand and minute hand when the minute value is in mixed fraction form, you need to follow these steps:

1. Convert the mixed fraction into an improper fraction.Example: For 7:30 2/11, the minute value is 30 2/11.
   To convert 30 2/11 into an improper fraction:
   - Multiply the denominator by the whole number:
   11 × 30 = 330
   - Add the numerator to the result:
   330 + 2 = 332
   - So, 30 2/11 becomes 332/11.
2. Apply the angle formula
   The formula to calculate the angle between the hour hand and minute hand is:
   (60H - 11M) / 2
   Where:
   H = Hour
   M = Minute (in improper fraction form)
3. Substitute the values into the formula:
   For 7:30 2/11:
   
   • Hour hand:
     60H = 60 × 7 = 420
   • Minute hand:
     11M = 11 × (332/11) = 332
4. Calculate the difference:
   Now, substitute the values into the formula:
   (420 - 332) / 2
   420 - 332 = 88
   88 / 2 = 44°So, the inner angle between the hour and minute hands is 44°.
5. Calculate the outer angle:
   Subtract the inner angle from 360°:
   360° - 44° = 316°

For 7:30 2/11, the two possible angles are:
- Inner angle = 44°
- Outer angle = 316°

This method works for any mixed fraction minute value. Just convert it to an improper fraction and apply the formula to find both the inner and outer angles.

Question 6

What is the speed of the Hour hand and Minute hand in a clock?

Answer 6

Answer:
-The speed of the hour hand is 1/2° per minute
-The speed of the minute hand is 6° per minute.

These are the fixed speeds of the hands in any clock calculation.

Explanation:

• Hour Hand Speed Calculation:
  The hour hand makes a full rotation of 360 degrees in 12 hours. So, in 1 hour, it moves 360 / 12 = 30 degrees.
  In 1 minute, the hour hand moves 30 / 60 = 1/2 degree.
• Minute Hand Speed Calculation:
  The minute hand makes a full rotation of 360 degrees in 60 minutes.
  In 1 minute, the minute hand moves 360 / 60 = 6 degrees.

So, the hour hand speed is 1/2 degree per minute and the minute hand speed is 6 degrees per minute.

Question 7

How to calculate the angle between the hour hand and minute hand between two different times?

Answer 7

Answer:
To calculate the angle between the hour hand and minute hand between two different times, follow these steps:

1. Find the difference in time:
   Subtract the earlier time from the later time to find the difference.
   Example: From 6:30 to 8:00.
   8:00 - 6:30 = 1 hour 30 minutes = 90 minutes.
2. Calculate the angle of the hour hand:
   Multiply the difference in time (in minutes) by the speed of the hour hand, which is 1/2 degree per minute.
   90 minutes × 1/2 degree = 45 degrees.
3. Calculate the angle of the minute hand:
   Multiply the difference in time (in minutes) by the speed of the minute hand, which is 6 degrees per minute.
   90 minutes × 6 degrees = 540 degrees.

Explanation:
- The angle of the hour hand between 6:30 and 8:00 is 45 degrees.
- The angle of the minute hand between 6:30 and 8:00 is 540 degrees.

Question 8

What are the day codes for calendar calculation?

Answer 8

Answer:
The day codes for calendar calculation are:
- Sunday: 0
- Monday: 1
- Tuesday: 2
- Wednesday: 3
- Thursday: 4
- Friday: 5
- Saturday: 6

Question 9

What are the month codes for normal year and leap year used in calendar calculation?

Answer 9

Answer:
Here is a combined format where the first digit represents the normal year code, and the second digit represents the leap year code:

• January: 00
• February: 33
• March: 34
• April: 60
• May: 12
• June: 45
• July: 60
• August: 23
• September: 56
• October: 01
• November: 34
• December: 56

• For normal years, use the first digit.
• For leap years, use the second digit.

For example:
- February: 3 is normal year code; and another 3 is leap year code.
- March: 3is normal year code; and 4 is leap year code.

Tips:
The below months are friends that shares the same code:
1. March and November: 34
2. April and July: 60
3. September and December: 56

Question 10

What is the formula for finding year code, which is further used in calendar calculation?

Answer 10

Formula:
Year Code = The reminder of {last 2 digit of the year + round value of (last 2 digit of the year / 4) / 7}

A same Step-by-Step Calculation to find yead code for 1989:

1. Last two digits of the year:
   The last two digits of 1989 are 89.
2. Divide the last two digits by 4:
   89 / 4 = 22 (round value).
3. Add the last two digits and the result of the division:
   (89 + 22 = 111)
4. Find the Reminder of 111/ 7:
   Remainder of 111/ 7 = 7 can come 15 times in 111 i.e. 7x12 = 105 (this is maximum dividable number by 7 before 111) and the balance i.e. reminder is 111 - 105 = 6
5. Year Code:
   The year code for 1989 is 6.

Question 11

What is the formula for finding any day of a calendar?