A rope can make 70 rounds of the circumference of a cylinder whose radius of the base is 14 cm. how many times can it go round a cylinder having radius 20 cm?

Let the mother's age 2 years ago be 4x and daughter's age 2 years ago be be x.
? (4x + 8) - (x + 8) = 12
? 3x = 12
? x = 4
? Mother's present age = 4x + 2 = 18 years
and daughter's present age = x + 2 = 6 years
? Required ratio = 3 : 1

Let the present age of the son be x and that of the father be 4x years.
? (x - 5) + (4x - 5) = 60
? 5x = 70
? x = 14 years
? Father's present age = 4x = 56 years

Age of C < Age of A < Age of B

From question,
A = C + x ....(i)
B = A + x ....(ii)

From equation (i) and (ii)
A - B = C - A
? 2A = B + C
? A = (B + C) / 2

Given that sum of the ages of B and C is 40 years.
So, A = (B + C) / 2 = 40/2 = 20 Years

Let the present age of A is x and present age of B is y.
Therefore, x + y = 63 ....(i)
Difference of their ages is = (x - y) years.

When A was as old as B then, A's age was 'y; years and B's age was [y - (x - y)] = (2y - x) years.

Given that present age of A is twice the past age of B.
? x = 2(2y - x)
? 3x = 4y .....(ii)

From (i) and (ii)
x = 36 and y = 27

So the difference in age of A and B is 36 - 27 = 9 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

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.

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

? 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 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 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 .