## The sum of the digits of a 2-digit number is 7. If the digits are reversed, the new number increased by 3 equals 4 times the original n

Question

The sum of the digits of a 2-digit number is 7. If the digits are reversed, the new number increased by 3 equals
4 times the original number. Find the original number.​

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2 weeks 2021-11-15T09:26:53+00:00 2 Answers 0 views 0

Let the original number be

yx

; i.e., 10y+x. We know x+y=7. The number obtained by reversing the digits in

xy

, i.e., 10x+y. The second condition gives 10x+y−2=2(10y+x). Thus we have two equations:

x+y=7….(1)

8x−19y=2….(2)

Multiply the equation (1) by 19 and get

19x+19y=133.

Adding this to (2), we obtain 27x=135. This gives x=5. Hence y=7−x=7−5=2.

The required number is 25.

Step-by-step explanation:

x+y = 7, or

y = 7-x

Let the number be 10x+y

10y+x = 4(10x+y)-3, or

10(7-x)+x = 4(10x+7-x) -3

70 -10x+x = 40x+28–4x-3

40x-4x+10x-x = 70–28+3

45x = 45

x=1 and y = 6.

The numbers are 16 and 61. Answer

## AND ONES DIGIT NUMBER BE Y

ATQ

ORIGINAL NUMBER = 10X+Y

x+y=71

IF DIGITS ARE REVERSED THEN

NUMBER FORMED

10Y+X+3 = 4(10X+Y)

10Y+X+3=40X+4Y

6Y+3=39x2

we have 2 equations solving these

we get

6y+3=39x

6x+6y=42

-45x=-45

x=1

putting in equation 1 weget

y=6

hence the original no is 10×1+6

=16