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A number of two digits exceeds four times the sum of its digits by 6 and it is increased by 9 on

reversing the digits. Find the number.

Answer:

Let’s consider the digit at tens place as x

And let the digit at unit place be y

The number is 10 × x + y × 1 = 10x + y

So, reversing the number = 10 × y + x × 1 = 10y + y

Then according to the first condition, we have

10x + y = 4 (x + y) + 6

10x – 4x + y – 4y = 6

6x – 3y = 6

2x – y = 2 … (i)

And according to the second condition, we have

10x + y + 9 = 10y + x

10x – x + y – 10y = -9

9x – 9y = -9

x – y = -1 … (ii)

Now, subtracting (ii) from (i) we have

2x – y = 2

x – y = -1

(-)--(+)--(+)---

x = 3

Substituting the value of x in (i), we get

2(3) – y = 2

6 – y = 2

y = 6 – 2

y = 4

Therefore, the number is 10 x 3 + 4 = 30 + 4 = 34

"welcome to little q a video i am vineeth
your lido tutor
bringing you this question on your
screen
a number of two digits exceeds four
times the sum of its
digits by 6 and it is increased by 9 on
reversing the digits
so number plus 9 will give you the
reverse of the number
let us define the variables first
so let
tense digit bx
let
units or ones digits be
did it be
why
then the number is equal to
10x plus y and
reverse of the number is equal to
10 y plus x
now
from the first condition
we have the number exceeds
four times the sum of the digits
by 6 so this implies
10x plus y is equal to 4x
plus 4y plus 6.
this implies 6x minus 3y
is equal to 6. this is our first
equation
what is the second condition it is
increased by 9
so this is the number
and this is the reverse
when it is reversed the number is
increased by 9
right therefore we can say that
9x plus 9y
or rather 9x minus 9y
is equal to -9 we can take 9 common and
cancel
it x minus y is equal to minus one
now equation two into multiply it by
three
we get or rather multiply it by six
we get 6x
minus 6y is equal to -6
this is equation 3.
now subtracting
3 from 1
we get
6x minus 3y minus 6x plus 6y
is equal to 6 minus minus 6
right this implies 3y
is equal to twelve this implies y is
equal to
four replacing y in equation two
x minus four is equal to minus one
this implies x is equal to 3
therefore the number is
10 into 3 30 plus 4 34.
isn't that easy guys if you still have
it out please leave a comment below
do like the video and subscribe to our
channel i'll see you in our next video
until then bye kids keep practicing keep
flourishing
"

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