In a two-digit number, ten's digit is twice the unit's digit. The number formed by interchanging the digits is $36$ less than the original number. The original number is _________.

48

No worries! We‘ve got your back. Try BYJU‘S free classes today!

70

No worries! We‘ve got your back. Try BYJU‘S free classes today!

72

No worries! We‘ve got your back. Try BYJU‘S free classes today!

84

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $84$
Let $X Y$ be the two digit number
$X = 2 Y$ ..........(1)
Number formed by exchanging the digit is $Y X$ .
$Y X = X Y - 36$ ...........(2)
Expanding the two digit numbers
$10 Y + X = 10 X + Y - 36$ .........(3)
$\Rightarrow 9 (Y - X) = - 36$
Substituting from (1), we get
$\Rightarrow Y = 4$
and $X = 8$
So, the number is 84.

Suggest Corrections

Similar questions

In a two digit number, ten’s digit is twice the unit’s digit. The number formed by interchanging the digits is 36 less than the original number. Find the number.

Q. In a two digit number, the digit at the unit's place is

1

less than twice the digit at the ten's place. If the digit at unit's and ten's place are interchanged, the difference between the new and the original number is less than the original number by

20

. The original number is

Q. In a two digit number unit's digit is 3 more than the ten's digit. The number formed by interchanging the digits and original number the digits and the original number are in the ratio 7 : 4. Find the number .

Q. In a two digit number unit's digit is 3 more than ten's digit. The number formed by interchanging the digits and the original number are in the ratio 7:4. Find the number.

In a two – digit number, the digit in the unit's place exceeds twice the digit in the ten's place by 1. If the digit in the unit’s place and the ten’s place are interchanged, then the difference between the newly formed number and the original number is less than the original number by 1. What is the original number?

Join BYJU'S Learning Program

In a two-digit number, ten's digit is twice the unit's digit. The number formed by interchanging the digits is 36 less than the original number. The original number is _________.

The correct option is D 84Let XY be the two digit number X=2Y ..........(1)Number formed by exchanging the digit is YX.YX=XY−36 ...........(2)Expanding the two digit numbers10Y+X=10X+Y−36 .........(3)⇒9(Y−X)=−36Substituting from (1), we get⇒Y=4and X=8So, the number is 84.

In a two-digit number, ten's digit is twice the unit's digit. The number formed by interchanging the digits is $36$ less than the original number. The original number is _________.