The total of the ages of Amar, Akbar and Anthony is 80 years. What was the total of their ages three years ago?

Let x and y be the ten's and unit's digits respectively of the numeral denoting the woman's age.

Then, woman's age = (10X + y) years; husband's age = (10y + x) years.

Therefore (10y + x)- (10X + y) = (1/11) (10y + x + 10x + y)

⟺ (9y-9x) = (1/11)(11y + 11x) = (x + y) ⟺ 10x = 8y ⟺ x = (4/5)y

Clearly, y should be a single-digit multiple of 5, which is 5.

So, x = 4, y = 5.

Hence, woman's age = 10x + y = 45 years.

Let d and s represent the number of daughters and sons respectively.

Then, we have :

d - 1 = s and 2 (s - 1) = d.

Solving these two equations, we get: d = 4, s = 3.

Total runs scored = (36 x 5) = 180.

Let the runs scored by E be x.

Then, runs scored by D = x + 5; runs scored by A = x + 8;

runs scored by B = x + x + 5 = 2x + 5;

runs scored by C = (107 - B) = 107 - (2x + 5) = 102 - 2x.

So, total runs = (x + 8) + (2x + 5) + (102 - 2x) + (x + 5) + x = 3x + 120.

Therefore 3x + 120 =180 ⟺ 3X = 60 ⟺ x = 20.

L.C.M. of 6, 5, 7, 10 and 12 is 420.

So, the bells will toll together after every 420 seconds i.e. 7 minutes.

Now, 7 x 8 = 56 and 7 x 9 = 63.

Thus, in 1-hour (or 60 minutes), the bells will toll together 8 times, excluding the one at the start.

Total number of digits

= (No. of digits in 1- digit page nos. + No. of digits in 2-digit page nos. + No. of digits in 3- digit page nos.)

= (1 x 9 + 2 x 90 + 3 x 267) = (9 + 180 + 801) = 990.

Since there are socks of only two colours, so two out of any three socks must always be of the same colour.

Since one of the numbers on the dial of a telephone is zero, so the product of all the numbers on it is 0.

We have : A = 3B ...(i) and

C - 4 = 2 (A - 4) ...(ii)

Also, A + 4 = 31 or A= 31-4 = 27.

Putting A = 27 in (i), we get: B = 9.

Putting A = 27 in (ii), we get C = 50.

When Ravi's brother was born, let Ravi's father's age = x years and mother's age = y years.

Then, sister's age = (x - 28) years. So, x - 28 = 4 or x = 32.

Ravi's age = (y - 26) years. Age of Ravi's brother = (y - 26 + 3) years = (y - 23) years.

Now, when Ravi's brother was born, his age = 0 i.e. y - 23 = 0 or y = 23.