Question

a two digit number is six times the sum of its digits. If the digit in the units place is increased by 2 and the digit in the tens place is decreased by 2 then the number soformed is 4 times the sum of its digits. Find the orignal number.

Answer 1

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Answer 2

Answer:

54

Step-by-step explanation:

Let units place digit y and tens place be x

A two digit number is six times the sum of its digits

So,$10x+y=6(x+y)$---A

If the digit in the units place is increased by 2 and the digit in the tens place is decreased by 2 then the number so formed is 4 times the sum of its digits.

$10(x-2)+y+2=4(x+2+y-2)$

$10(x-2)+y+2=4(x+y)$---B

Plot A and B on graph

$10x+y=6(x+y)$ -- Black line

$10(x-2)+y+2=4(x+y)$---Red line

Intersection point provides the answer

So, intersection point  (5,4)

So,x=5 , y = 4

So, Original number is 54