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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.

• Solution

• Transcript

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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