? 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
Relative speed = (84 + 60) km/h = 144 km/h = 144 x (5/18) = 8 m/s
Distance covered in passing each other = 512 + 528 = 1040 m
? Required time = 1040/40 = 26 s
Let the present age of Kunal be 3x year and the
present age of Ganesh = 5x years.
According to question ,
(5x + 4 ) - (3x + 4 ) = 12
? 2x = 12
? x = 6
? Present age of Kunal = 3x = 3 x 6 = 18 year
Let the present age of Pradhan be P years and his father's age = Q years.
From 1st condition,
(P + 6) = (Q + 6 ) x 3/7
? 7P + 42 = 3Q + 18
? 7P - 3Q = -24 ...(i)
From 2nd condition
(P - 10) / (Q - 10) = 1/5
? 5P - 50 = Q - 10
? 5P - Q = 40 .....(ii)
Multiplying equation (ii) by 3 and subtracting from (i) we get
P = 18, Q = 50
So present age of Pradhan's father = 50 years.
P + R + 2 Q = 59, ....(i)
Q + R + 3 P = 68 .....(ii)
and P + 3 (Q + R) = 108 ......(iii)
Solving the above three equations, we get
? P + 3 (68 - 3P) = 108
? P + 204 - 9P = 108
? P = 12 years.
Let the ages of Harish and Seema be x and y respectively.
According to the question,
xy = 240 ....(i)
2y - x = 4 ....(ii)
Solving equations (i) and (ii), we get
y = 12 years
? 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
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
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
? 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 Raman's daughter = N yr
Then, age of Raman's = 3N yr
and age of Raman's mother = (13/9) x 3N = 13N/3 yr
According to the question, N + 3N + 13N/3 = 125
? 3N + 9N + 13N = 125 x 3
? N = (125 x 3)/25 = 15
Hence, required difference = 13N/3 - N = 10N/3
= (10 x 15)/3 = 50 yr
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