Question

4. A number consists of two-digits. 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.
Find the number.

Answer 1

Answer:

Step-by-step explanation:

original number

Suppose, tens digit = x then unit digit = 3x

value of 10s digit = 10x 

value of 1s digit = 3x

number = 10x + 3x = 13x

REVERSEd NUMBER

10s digit = 3x and 1s digit = x

value of 10s digit = 30x

value of 1s digit = x

number = 30x + x = 31x

relation between original and reversed number

According to condition

original number + 36 = reversed number

13x + 36 = 31x

36 = 31x - 13x

36 = 18x

36/18 = x

x = 2

now:- original number = 13x = 13*2 = 26

          reversed number = 62

Answer 2

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