# Seven times a two

Given:Seven times a two-digit number is equal to four times the number obtained by reversing the digits and the difference between the digits is 3.

To find: the number.

Solution:

Let the one’s digit be ‘a’ and ten’s digit be ‘b’.

The the number will be 10b+a

If the digits are reversed the number will be 10a+b

Given, seven times a two-digit number is equal to four times the number obtained by reversing the digits.

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

⇒ 7(10b) + 7a = 4(10a)+ 4b

⇒ 70b + 7a = 40a + 4b

⇒ 70b - 4b =  40a - 7a

66b = 33a

a = 2b ----- (1)

Also, difference between the digits is 3

a – b = 3

Substitute value of a from (1)

2b – b = 3

Thus, b = 3

a = 2 × 3 = 6

The number is 10b+a = 10(3)+6 = 36

∴ Number is 36.

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