Question

Ashok, a maths teacher in the school, asked his students to guess his date of birth by giving the following hints.
Hint 1: He was born in 1995
Hint 2: The sum of the products of his birth date multiplied by 24 and his birthday month multiplied by 60 is 1284.
Find the sum of Ashok's birth date, birth month, and birth year.

• A. 2032
• B. 2023
• C. 2035
• D. 2033
• E. 2030

Answer 1

Answer: (A)

2032

Answer 2

Let Ashok be born on the $x^{th}$ day of the $y^{th}$ month in $1995$.
Given that,

$24x+60y = 1284$

$2x+5y = 107$

$y$ = $\frac{107-2x}{5}$ = $21+\frac{2(1-x)}{5}$

$(1 – x)$ must be a multiple of $5$.
As $1≤x≤31$, $1≤y≤12$

Then, the only values of $(x, y)$ satisfying the equation and other conditions are $(26, 11)$ and $(31, 9)$.

Thus, the birthday can be on $26$ November or $31$ September.

As September does not have $31$ days, this case is rejected.

Thus, the required sum = $26 + 11 + 1995 = 2032$

Hence, option A is the correct answer.