Answer :
To find the 2-digit number where the tens digit is twice the one's digit and reversing the digits gives a number 27 less than the original:
- Let the one's digit be [tex]x[/tex].
- Then the tens digit is [tex]2x[/tex].
- The number can be expressed as [tex]10(2x) + x[/tex] or [tex]21x[/tex].
- When the digits are reversed, the new number is [tex]10x + 2x = 12x[/tex].
- According to the problem, [tex]21x - 12x = 27[/tex].
- Solving gives [tex]9x = 27[/tex], so [tex]x = 3[/tex].
- Thus, the original number is [tex]21 \times 3 = 63[/tex].
To find the angle between the hour and minute hands at 10:15:
- The minute hand is at 15 minutes, which is at [tex]15 imes 6 = 90[/tex] degrees from the 12.
- The hour hand at 10:15 is [tex]10 imes 30 + 15 imes 0.5 = 307.5[/tex] degrees from the 12.
- The difference between them is [tex]307.5 - 90 = 217.5[/tex] degrees.
- However, the smaller angle between them is [tex]360 - 217.5 = 142.5[/tex] degrees.
The missing term in the pattern A, C, F, J, ?, T:
- The pattern skips 1, 2, 3, and 4 letters respectively: A (1), C (+2), F (+3), J (+4), now add 5.
- After J is J+5=O (skipping K, L, M, N).
- Thus, the missing term is O.
To find Tom's current age:
- Let Tom's current age be [tex]t[/tex], so his father is [tex]2t[/tex].
- Ten years ago, Tom was [tex]t - 10[/tex] and his father was [tex]2t - 10[/tex], which was 3 times Tom's age.
- So, [tex]2t - 10 = 3(t - 10)[/tex].
- Solving this: [tex]2t - 10 = 3t - 30[/tex] leads to [tex]20 = t[/tex].
- Thus, Tom is 20 years old.
To measure exactly 4 L using a 3 L jug and a 5 L jug:
- Fill the 5 L jug completely.
- Pour from the 5 L jug into the 3 L jug until it's full, leaving 2 L in the 5 L jug.
- Empty the 3 L jug, and transfer the 2 L from the 5 L jug to the 3 L jug.
- Fill the 5 L jug again.
- Pour from the 5 L jug into the 3 L jug until it fills up (1 L needed), thus leaving exactly 4 L in the 5 L jug.