In a two digit number. The units digit is thrice the tens digit. If 36

1.	In a two digit number. The units digit is thrice the tens digit. If 36 is added to the number, the digits interchange their place. Find the number.
Answer» ⠀⠀⠀ ՏϴᏞႮͲᏆϴΝ $\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$ Let the digit in the units place is x. And the digit in the tens place be y. Then x = 3y and the NUMBER = 10y + x The number obtained by reversing the digits is 10X + y. If 36 is added to the number, digits interchange their PLACES, THEREFORE, We have: 10y + x + 36 = 10x + y ➠ 10y – y + x + 36 = 10x + y - y ➠ 9y + x – 10x + 36 = 10x - 10x ➠ 9y - 9x + 36 = 0 or, 9x - 9y = 36 ➠ 9(x - y) = 36 ➠ 9(x - y)/9 = 36/9 ➠ x - y = 4 ………. (i) Substituting the value of x = 3y in equation (i), We get: 3y - y = 4 ➠ 2y = 4 ➠ y = 4/2 ➠ y = 2 Substituting the value of y = 2 in equation (i), We get: x - 2 = 4 ➠ x = 4 + 2 ➠ x = 6 Hence, the number becomes 26. $\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

In a two digit number. The units digit is thrice the tens digit. If 36 is added to the number, the digits interchange their place. Find the number.

Answer»

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Then x = 3y and the NUMBER = 10y + x

The number obtained by reversing the digits is 10X + y.

If 36 is added to the number, digits interchange their PLACES,

THEREFORE, We have:

➠ 10y – y + x + 36 = 10x + y - y

➠ 9y + x – 10x + 36 = 10x - 10x

➠ 9y - 9x + 36 = 0 or, 9x - 9y = 36

➠ 9(x - y) = 36

➠ 9(x - y)/9 = 36/9

➠ x - y = 4 ………. (i)

Substituting the value of x = 3y in equation (i),

3y - y = 4

➠ 2y = 4

➠ y = 4/2

➠ y = 2

Substituting the value of y = 2 in equation (i),

x - 2 = 4

➠ x = 4 + 2

➠ x = 6

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