The ratio of a two-digit natural number to a number formed by reversing its digits is 4:7

Ratio Proportion Numbers

The ratio of a two-digit natural number to a number formed by reversing its digits is 4:7. The number of such pairs is

  1. 5
  2. 4
  3. 3
  4. 2

Answer

Let the digit at unit's place be a.

Let the digit at ten's place be b.

Original number = 10b + a

Number formed on reversing the digits = 10a + b

According to the question,

10b + a : 10a + b = 4 : 7

70b + 7a = 40a + 4b

2b = a

When b = 1, a = 2; numbers are 12 and 21.

When b = 2, a = 4; numbers are 24 and 42.

When b = 3, a = 6; numbers are 36 and 63.

When b = 4, a = 8; numbers are 48 and 84.

When b = 5, number become three-digit number.

Therefore, only 4 pairs are possible.

The correct option is B.