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 of the digits is 3, determine the
number​

Answer 1

Answer:

The required number is 36

Step-by-step explanation:

Let x be the digits in 10s place of the number

Let y be the digits in 1s place of the number

Hence, the number is 10x + y

The number obtained by reversing the digits is 10y + x

ATQ,

7(10x + y) = 4(10y + x)

70x + 7y = 40y + 4x

66x - 33y = 0

2x - y = 0 ........Eqn 1

Also given that, the difference in digits is 3

=> y - x = 3 ....Eqn 2

Substituting for "x" from Eqn 2 in Eqn 1, we get:

2(y - 3) - y = 0

2y - 6 - y = 0

y - 6 = 0

y = 6

Using Eqn 2, we get:

6 - x = 3

=> x = 3

The required number is 10x + y = 10*3 + 6 = 30 + 6 = 36

Verify:

Original number = 36

Difference in digits = 6-3 = 3 (verified)

Reversed number = 63

Seven times original number = 7*36 = 252

Four times reversed number = 4*63 = 252

Thus, verified.

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.