JAMIA 2026 — Mathematics PYQ

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Question

JAMIA 2026 — Mathematics PYQ

JAMIA | Mathematics | 2026

The sum of digits of a two digit number is $15$ . The number obtained by interchanging the digits exceeds the given number by $9$ . The number is.

Choose the correct answer:

Explanation

Step 1: Set up the first equation (Sum of digits)

The sum of the digits is $15$ :

$x + y = 15 — (Equation 1)$

Step 2: Set up the second equation (Interchanging digits)

The number obtained by interchanging the digits exceeds the original number by $9$ :

$Reversed Number - Original Number = 9$

$(10 y + x) - (10 x + y) = 9$

Simplify the expression:

$10 y + x - 10 x - y = 9$

$9 y - 9 x = 9$

Divide the entire equation by $9$ :

$y - x = 1$

$- x + y = 1 — (Equation 2)$

Step 3: Solve the system of linear equations

Add Equation 1 and Equation 2:

$(x + y) + (- x + y) = 15 + 1$

$2 y = 16$

$y = \frac{16}{2}$

$y = 8$

Substitute $y = 8$ back into Equation 1:

$x + 8 = 15$

$x = 15 - 8$

$x = 7$

Step 4: Form the original number

Substitute the values of tens digit ( $x = 7$ ) and units digit ( $y = 8$ ) into the original number form:

$Original Number = 10 x + y = 10 (7) + 8 = 78$