Question

Seven times a two-digit number is equal to four times the number obtained
by reversing the order of its digits. If the difference between the digits is 3,
find the number.​

Answer 1

$\bf{\huge{\underline{\boxed{\sf\pink{Answer:\:36}}}}}$

Given :

• Seven times a two -  digit number is equal to 4 times reverse of the given number.
• Difference between the digits is 3.

To Find :

• The unknown number.

$\huge\underline\green{\tt Solution:}$

Let the number be PQ, P in the tens place and Q in the ones place.

So,

Number = 10P + Q [ As stated above, P is in tens place ]

After reversing the order of it's digits,

Number = 10Q + P

Now,

                   According to Question

7 ( 10P + Q ) = 4 ( 10Q + P )

⇒ 70P + 7Q = 40Q + 4P

⇒ 70P - 4P = 40Q - 7Q

⇒ 66P = 33Q

⇒ P = $\dfrac{33Q}{66P}$

∴  $P = \dfrac{Q}{2}$ ____________ ( ! )

→ Difference between the digits is 3

So,

P - Q = 3 _________ ( !! )  [ we can't use this equation, reason is stated below ]

Q - P = 3 ________ ( !!! )

But,  P = $\dfrac{Q}{2}$ . It means P is smaller than Q.

$Q - \dfrac{Q}{2} = 3$

⇒ $\dfrac{Q}{2} = 3$

⇒ $Q = 6$

→ Put this value in equation ( !!!)

→  $P = \dfrac{Y}{2}$

→ $P = \dfrac{6}{2}$

∴ P = 3

Hence,

P = 3 and Q = 6

So,

Number = 36.

Answer : The required  number is 36.

Answer 2

Answer:

36

Step-by-step explanation:

Let the unit digit be a and tenth unit be b .

So , number = 10 b + a

It's said number is seven times is equal to reversing the order of its digit.

= > 7 ( 10 b + a ) = 4 ( 10 a + b )

= > 70 b + 7 a = 40 a + 4 b

= > 66 b = 33 a

= > a = 2 b ... ( i )

Also given numbers' difference is 3 .

a - b = 3  ( ii )

From ( i ) and ( ii ) we get :

a b - b = 3

b = 3

= > a = 6

Hence number = > 30 + 6

= > 36.