4. A number consists of two-digits. The digit at the units place is 3

1.	4. A number consists of two-digits. The digit at the units place is 3 times thedigit at the tens place. If 36 is added to the number, the digits are reversed.Find the number.
Answer» ANSWER: Original number = 26 GIVEN: The digit at the units place is 3 TIMES the digit at the tens place. If 36 is added to the number, the DIGITS are reversed. TO FIND: Orginal number SOLUTION: Let the digit at tens place be x. Let the digit at unit place be y. ORIGINAL NUMBER = 10x+y According to the question: CASE 1 $\implies \: y = 3 \times x \\ \implies \: y = 3x \: \: \: \: ....(i)$ CASE 2 REVERSED NUMBER = 10y+x $\implies \: 10x + y + 36 = 10y + x \\ \implies 10x - x + y - 10y = - 36 \\ \implies \: 9x - 9y = - 36 \\ \implies \: 9(x - y) = - 36 \\ \implies \: x - y = \frac{ - 36}{9} \\ \implies \: x - y = - 4 \\ \\ putting \: y = 3x \: from \: eq(i) \\ \implies \: x - 3x = - 4 \\ \implies \: - 2x = - 4 \\ \implies \: x = 2 \\ \\ \implies \: y = 3x \\ \implies \: y = 3 \times 2 \\ \implies \: y = 6$ So original number = 10x+y = 10*2 + 6 =26

4. A number consists of two-digits. The digit at the units place is 3 times thedigit at the tens place. If 36 is added to the number, the digits are reversed.Find the number.

Answer»

GIVEN:

The digit at the units place is 3 TIMES the digit at the tens place.
If 36 is added to the number, the DIGITS are reversed.

SOLUTION:

Let the digit at tens place be x.
Let the digit at unit place be y.

ORIGINAL NUMBER = 10x+y

According to the question:

CASE 1

$\implies \: y = 3 \times x \\ \implies \: y = 3x \: \: \: \: ....(i)$

CASE 2

REVERSED NUMBER = 10y+x

$\implies \: 10x + y + 36 = 10y + x \\ \implies 10x - x + y - 10y = - 36 \\ \implies \: 9x - 9y = - 36 \\ \implies \: 9(x - y) = - 36 \\ \implies \: x - y = \frac{ - 36}{9} \\ \implies \: x - y = - 4 \\ \\ putting \: y = 3x \: from \: eq(i) \\ \implies \: x - 3x = - 4 \\ \implies \: - 2x = - 4 \\ \implies \: x = 2 \\ \\ \implies \: y = 3x \\ \implies \: y = 3 \times 2 \\ \implies \: y = 6$

So original number = 10x+y

= 10*2 + 6

=26