Topic

Playing with Numbers

Given

In a five digit number, the digit at the hundreds place is three-fourth of the digit at ten thousands place and the digit at tens place is two-third of the digit at hundreds place. The digit at tens place is square of the smallest prime number and the digit at thousands place is the largest single digit prime number. If the digit at unit place is the largest single digit odd number.

To Find

The required number.

Solution

Let five digit number be in FORM of abcde.

e is at ONES place.

d is at tens place.

c is at hundreds place.

b is at thousands place.

a is at ten thousands place.

It is given that

The digit at the hundreds place is three-fourth of the digit at ten thousands place.

c = ( 3/4 )a

The digit at tens place is two-third of the digit at hundreds place.

d = ( 2/3 )c

The digit at tens place is square of the smallest prime number.

d = Square of Smallest prime number

Smallest prime number = 2

d = 2²

d = 4

And if d = 4 then

4 = ( 2/3) c

c = ( 4 × 3 ) / 2

c = 6

And if c = 6 then

6 = ( 3/4 )a

a = ( 4 × 6 ) / 3

a = 24 / 3

a = 8

The digit at thousands place is the largest single digit prime number.

b = Largest Single digit prime number

Largest Single digit prime number = 7

b = 7

If the digit at unit place is the largest single digit odd number.

e = Largest single digit odd number

Largest single digit odd number = 9

e = 9

So, digits are,

a = 8

b = 7

c = 6

d = 4

e = 9

Answer

So, the required five digit number is 87649 which is option 3.