Question

# A number which is formed by two digits is 3 times the sum of the digits. While interchanging the digits it is 45 more than the actual number. Find the number.

Hint:

### let the number be xy i. e 10x + y = xy where x and y are digits of the number

Given The number formed is 3 times the sum of digits (i. e 10x+y =3(x + y))

If digits are reversed the number is increased by 45 (i. e xy +45 = yx)

## The correct answer is: 27

### Ans :- 27 is the number which satisfies the given condition.

Explanation :-

Step 1:- frame the equations from the given set of conditions .

Given The number formed is 3 times the sum of digits

— Eq1

If digits are reversed the number is reduced by 45

—- Eq2

Step 2:- Substitute Eq1 in Eq2

We get

∴ x = 2

Step 3:- find the value of y by substituting x=2 in Eq2

∴ y = 7

∴ 27 is the number which satisfy the given conditions.

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