Question

please solve this with showing the working

The sum of the digits of a two-digit number is 15. If the number formed by reversing the digits is less than the original number by 27, find the original number.​

Answer 1

Answer:

let the number of two digits be 10x+y

Now,

sum of the two digits is 15

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

no. after reversing the digits:

(10y+x)(10x+y)-(10y+x)=27

9x-9y=27

x-y=3-----------(2)

by solving equations 1 and 2,

We get x=9 and y=6 therefore,

the original no. is 10(9)+6=96

Answer 2

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Sol:

Let the number with two digits be 10x + y.

Sum of the digits is 15.

⇒ x + y = 15 ----------------- (1)

Number formed by reversing the digits = (10y + x)

(10x + y) - (10y + x) = 27

⇒ 9x - 9y = 27

⇒ x - y = 3 ----------------- (2)

Solving equations (1) and (2), we get x = 9 and y = 6.

Therefore, the original number is 10(9) + 6 = 96.

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