Raman's present age is three times his daughter's and nine-thirteenth of his mother's present age. The sum of the present ages of all three of them is 125 yr. What is the difference between the present ages of Raman's daughter and Raman's mother?

? Total age of Sachin and Saurabh = 36 x 2 = 27 yr
Let age of Saurabh = x yr
Then, age of Sachin = (x + 8) yr
According to the question, x + x + 8 = 72
? 2x = 64
? x = 32
Hence, Saurabh's present age = 32 yr

Let age of Purvi = N yr
Then, age of Anil = 1.5N yr
According to the question,
(1.5N + 8)/(N + 8) = 25/18
? 27N + 144 = 25N + 200
? N = 56/2 = 28
Hence, present age of Purvi = 28 yr

Let the present age of Varun be M and present age of Kapil be N.
According to the questions,
M + N = 42 ...(i)
Again, according to the question, After 5 yr,
(M + 5)/(N + 5) = 15/11
? 11M + 55 = 15N + 75
? 11M - 15N = 20 ...(ii)

On solving Eqs. (i) and (ii),
? N = 17 yr
Hence, present age of Kapil = 17 yr

? Total age of 9 students and a teacher = 10 x 16 = 160 yr
Total age of first 4 students = 4 x 19 = 76 yr
and total age of last 5 students = 5 x 10 = 50 yr
? Age of teacher = 160 - 76 - 50 = 34 yr

? Total age of father and mother = 35 x 2 = 70 yr
and total age of father, mother and son = 27 x 3 = 81 yr
&there4: Age of son = 81 -70 = 11 yr

Let the present ages of Maya and Chhaya are 6N and 5N yr. respectively.

According to the question, After 15 yr,
(6N + 15) / (5N + 15) = 9/8
? 48N + 120 = 45N + 135
? N = 5
Hence, present age of Maya = 5 x 6 = 30 yr

Let the present ages of Manoj and Wasim are 3k yr and 11k yr, respectively.
According to the question ,
11k = 85 - 7 - 12
? 11k = 66
? k = 6
? Present age of Manoj = 3 x 6 = 18 yr
Hence, present age of Manoj's father = 18 + 25 = 43 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

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

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 .