The ratio of ages of Mohan and Sohan is 3 : 4. Four years ago the ratio was 5 : 7. Find the present ages of Mohan and Sohan.

When Ravi was born, his mother's age was 26 yr and his elder brother was 3 yr elder to him.
? Mother's age when brother was born
= 26 - 3 = 23 yr
Ravi's father was 28 yr of age when his sister was born and his sister was 4 yr of age when his brother was born
? Age of father when brother was born
= 28 + 4 = 32 yr

Let ages of man and his son are 8k yr and k yr, respectively .
According to the question,
(8k + k)/2 = 27
? k = (27 x 2)/9 = 6
Hence, age of son after 6 yr = 6 + 6 = 12 yr

Let Arnav's age = k yr
Then, Palash's age = 3k yr
Acoording to the question, 3k + 7 = 2(k + 7)
? 3k + 7 = 2k + 14
? k = 7

? Age of Arnav after 14 yr = 7 + 14 = 21 yr
and Palash's present age = 21 yr

Hence, Palash's age is one time of Arnav's age .

4 yr ago, let Ram's age = k yr and Shyam's age = 3k/4 yr
Now, Ram's present age = (k + 4) yr
and Shyam's present age = (3k/4 + 4) yr
According to the question, 5/6(k + 4 + 4) = (3k/4 + 4 + 4)
? 4 (5k + 40) = 6(3k + 32)
? 20k + 160 = 18k + 192
? 2k = 32
? k = 16
Hence, present age of Shyam = (3/4) x 16 + 4 = 16 yr

? Total age of five members of a family = 24 x 5 = 120
? Total age of four members at the time of birth of youngest = 120 - 8 x 5
= 120 - 40 = 80 yr
Hence, required average age = 80/4 = 20 yr

For two years having same calendar must have two common conditions: both having same length in terms of number of days and first day of the week.

The year 1991 has 365 days,,that is 1 odd day , year 1992 has 366 days , i.e. 2 odd days , year 1993 has 365 days i.e. 1 odd day. the years 1994,1995,1996 have 1 odd day each.

the sum of odd days so calculated from year 1990 to 1996 .
(1+2+1+1+1+1)=7 odd days. 5

hence, the year 1997 will have same calendar as that of year 1990.

Each day of the week is repeated after 7 days
? After 63 days, it would be Friday
So, After 62 days, it would be Thursday

The year 1984 being a leap year, it has 2 odd days. So, the day on 2nd July, 1985 is two days beyond the day on 2nd July, 1984. But, 2nd July 1985 was Wednesday.

? 2nd July, 1984 was Monday

No of days = Jan. + Feb. + March
30 + 28 + 15 = 73 days

Starting with 1988, we go on counting thye number of odd days till the sum is divisible by 7
Year 1988 odd days = 2
Year 1989 odd days = 1
Year 1990 odd days = 1
Year 1991 odd days = 1
Year 1992 odd days = 2

So total odd days = 7;
? Calendar for 1993 is the same as that of 1988.