Ashifur September 9, 2023 - 19:17
Problem: A two digit number is four times the sum of the two digits. If the digits are reversed, the number so obtained is 18 more than the original number. What is the original number?

View all: SONALI & JANATA BANK LTD (SO) IT WRITTEN QUESTION (MATH) SOLVE | 2018

Correct Answer: 24

Explanation:

Let. Tenth digit is x and unit digit is y

The number = (10x + y)

According to first condition, 4(x + y) = 10x + y ………(i)

And second condition, (10x + y) + 18 = 10y + x………………… (ii)

From equation (ii),

10x+4+y+18 = 10y +x

=> 9x-9y = -18 . .

=> 9y – 9x = 18

=> 9(y-x) = 18

= (y – x) = $\frac{18}{9}$ = 2

=> y – x = 2

so, y = x + 2 ……….(iii)

From equation (i) we get 4(x + y) = 10x + y

=> 4x + 4y = 10x + y

=> 3y =6x

=> y = 2

so, y = x+2………….(Iv)

From equation (i), we get 4(x+y) = 10x+y

=> 4x+4y = 10x+y

=> 3y = 6x

=> y = 2y

=> x+2 = 2x [ putting the value of y]

so, x=2

Now, putting the value of x in equation (iv) we get

y= x+2

=> y = 2+2 =4

so, y=4

The number is |(10x+y) = (10×2)+4 =20+4 =24

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