Question

In a five digit number, digit at ten's place is 4, digit at unit's place is one fourth of ten's place digit, digit at hundred's place is 0, digit at thousand's place is 5 times of the digit at unit's place and ten thousand's place digit is double the digit at ten's place. write the number.​

Answer 1

AnswEr:-

The number = 85,041

$\rule{200}{1}$

As there are five digits in the number.

Let the digits be m , n , p , q & r

∴ Number = m + 10n + 100p + 1000q + 10000r

$\rule{150}{2}$

Now digits in different positions are as follows:-

Digit at ten's place:-

⇒ 4

Digit at unit's place:-

⇒ ¼th of ten's place digit

⇒ ¼ × 4

⇒ 1

Digit at hundred's place:-

⇒ 0

Digit at thousand's place :-

⇒ 5 times unit's digit

⇒ 5 × 1

⇒ 5

Digit at ten thousand's place:-

⇒ 2 times digit at ten's place

⇒ 2 × 4

⇒ 8

So we get required values:-

⇒ m = 1

⇒ n = 4

⇒ p = 0

⇒ q = 5

⇒ r = 8

Now number:-

⇒ Number = 1 + 10(4) + 100(0) + 1000(5) + 10000(8)

⇒ Number = 1 + 40 + 0 + 5000 + 80000

⇒ Number = 85,041

Therefore,

Required number = 85,041

Answer 2

Given :

• In a five digit number, the ten's place digit is 4.
• Digit at the unit's place is ¼ of ten's place.
• Digit at hundred's place is 0.
• Digit at the thousand's place is 5 times of the digit at unit's place.
• Ten thousand's place digit is double the digit at ten's place.

To Find :

• The Five Digit Number.

Solution :

Let the digit at the ten thousand's place be v.

Let the digit at the thousand's place be w.

Let the digit at the hundred's place be x.

Let the digit at the ten's place be y.

Let the digit at the unit's place be z.

Original Number = $\bold{10000v\:+\:1000w\:+\:100x\:+\:10y\:+z}$

Case 1 :

The ten's place digit is 4.

Equation :

$\sf{y=4\:\:\:\:(1)}$

Case 2 :

The digit at the unit's place is ¼ of the digit in the ten's place.

Equation :

$\implies$ $\sf{z=\dfrac{1}{4}\:\times\:y}$

$\implies$ $\sf{z=\dfrac{1}{4}\:\times\:4}$

$\bold{\big[From\:equation\:(1)\:y\:=\:4}$

$\implies$ $\sf{z=\dfrac{4}{4}}$

$\implies$ $\sf{z=1\:\:\:\:(2)}$

Case 3 :

The hundred's place digit is 0.

Equation :

$\implies$ $\sf{x=0\:\:\:(3)}$

Case 4 :

The digit at the thousand's place is 5 times the digit at the unit's place.

Equation :

$\implies$ $\sf{w\:=\:5z}$

$\implies$ $\sf{w\:=\:5\:\times\:1}$

$\bold{\big[From\:equation\:(2)\:z\:=\:1\big]}$

$\implies$ $\sf{w=5\:\:\:\:(4)}$

Case 5 :

The digit at the ten thousand's place is double the digit at the ten's place.

Equation :

$\implies$ $\sf{v=2y}$

$\implies$ $\sf{v=2\:\times\:4}$

$\bold{\big[From\:equation\:(1)\:y\:=\:4\:\big]}$

$\implies$ $\sf{v=8}$

Five Digit Number :

$\implies$ $\sf{10000v+1000w+100x+10y+z}$

$\implies$ $\sf{10000(8)+1000(5)+100(0)+10(4)+1}$

$\implies$ $\sf{80000+5000+0+40+1}$

$\implies$ $\sf{80000+5000+41}$

$\implies$ $\sf{80000+5041}$

$\implies$ $\sf{85041}$

$\large{\boxed{\bold{\purple{Original\:Five\:Digit\:Number\:=\:85041}}}}$