The year next to 1990 having the same calendar as that of 1988 is

Options

A. 1990
B. 1992
C. 1993
D. 1995

Answer

To find the year next to 1990 that has the same calendar as that of 1988, we need to determine the number of odd days for the years in question. Here’s a step-by-step solution:

### Step-by-Step Solution:

1. **Identify the Year Types**:
- 1988 is a leap year. Leap years have 2 odd days.
- 1990 is a common year. Common years have 1 odd day.

2. **Calculate Odd Days for Subsequent Years**:
- **1989**: Common year → 1 odd day.
- **1990**: Common year → 1 odd day.
- **1991**: Common year → 1 odd day.
- **1992**: Leap year → 2 odd days.

3. **Sum of Odd Days from 1988 to 1992**:
- From 1988 to 1989: 2 (1988) + 1 (1989) = 3 odd days.
- From 1989 to 1990: 3 + 1 (1990) = 4 odd days.
- From 1990 to 1991: 4 + 1 (1991) = 5 odd days.
- From 1991 to 1992: 5 + 2 (1992) = 7 odd days.

4. **Check Divisibility by 7**:
- The total odd days from 1988 to 1992 is 7, which is divisible by 7. This means that 1992 has the same calendar as 1988.

5. **Continue to Find the Next Year**:
- **1993**: Common year → 1 odd day.
- **1994**: Common year → 1 odd day.
- **1995**: Common year → 1 odd day.
- **1996**: Leap year → 2 odd days.
- **1997**: Common year → 1 odd day.
- **1998**: Common year → 1 odd day.
- **1999**: Common year → 1 odd day.
- **2000**: Leap year → 2 odd days.

6. **Sum of Odd Days from 1992 to 2000**:
- From 1992 to 1993: 2 (1992) + 1 (1993) = 3 odd days.
- From 1993 to 1994: 3 + 1 (1994) = 4 odd days.
- From 1994 to 1995: 4 + 1 (1995) = 5 odd days.
- From 1995 to 1996: 5 + 2 (1996) = 7 odd days.
- From 1996 to 1997: 7 + 1 (1997) = 8 odd days.
- From 1997 to 1998: 8 + 1 (1998) = 9 odd days.
- From 1998 to 1999: 9 + 1 (1999) = 10 odd days.
- From 1999 to 2000: 10 + 2 (2000) = 12 odd days.

7. **Check Divisibility by 7 Again**:
- The total odd days from 1992 to 2000 is 12. When we reduce this by 7, we get 5 odd days.

8. **Continue Counting**:
- **2001**: Common year → 1 odd day.
- **2002**: Common year → 1 odd day.
- **2003**: Common year → 1 odd day.
- **2004**: Leap year → 2 odd days.

9. **Final Calculation**:
- From 2000 to 2001: 5 + 1 = 6 odd days.
- From 2001 to 2002: 6 + 1 = 7 odd days.
- From 2002 to 2003: 7 + 1 = 8 odd days.
- From 2003 to 2004: 8 + 2 = 10 odd days.

10. **Conclusion**:
- The total odd days from 1988 to 2004 is 10, which is not divisible by 7. However, if we check the year after 1990, we find that the year 1993 has the same calendar as 1988.

### Final Answer:
The year next to 1990 having the same calendar as that of 1988 is **1993**.