Question

In a 3-digit number, the tens digit is thrice the units digit and the hundreds digit is four times the units digit. Also, the sum of its digit is 16. Find the number.

Answer this please.​

Answer 1

Given:

• In a 3-digit number, the tens digit is thrice the units digit.

• The hundreds digit is four times the units digit.

• The sum of its digit is 16.

To calculate:

• The number.

Calculation:

Let us assume the units digit as x .

• $\sf {Units \: digit \to x }$

Then, according to question, the tens digit becomes 3x and the hundreds digit becomes 4x.

• $\sf {Tens \: digit \to 3x }$
• $\sf {Hundreds \: digit \to 4x }$

Also, the sum of its digits is 16 i.e,

$\sf { \longrightarrow Units \: digit +Tens \: digit + Hundreds \: digit = 16 }$

Substituting the values.

$\sf { \longrightarrow x +3x + 4x = 16 }$

Here, a suitable equation has been formed.We have to find the value of x , then we can find the number easily.

Performing addition in LHS.

$\sf { \longrightarrow 8x = 16 }$

Transposing 8 from LHS to RHS.

$\sf { \longrightarrow x = \dfrac{16}{8} }$

Performing division in RHS.

$\sf \red { \longrightarrow x = 2 }$

The value of x is 2. Now, lets find out the value of the digits.

$\sf { \longrightarrow Units \: digit = x } \\ \\ \sf { \longrightarrow Units \: digit = 2}$

_______

$\sf { \longrightarrow Tens \: digit = 3x} \\ \\ \sf { \longrightarrow Tens \: digit = 3(2)} \\ \\ \sf { \longrightarrow Tens \: digit = 6}$

______

$\sf { \longrightarrow Hundreds \: digit = 4x} \\ \\ \sf { \longrightarrow Hundreds\: digit = 4(2)} \\ \\ \sf { \longrightarrow Hundreds \: digit = 8}$

Hence,

$\sf { \longrightarrow Number = \underbrace{8}_{ Hundreds\: digit} \: \: \underbrace{6}_{Tens \: digit} \: \: \underbrace{2}_{ Units\: digit} \:} \\ \\ \sf \red { \longrightarrow Number = 862 }$

Answer 2

Given :-

• In a 3-digit number, the tens digit is thrice the units digit and the hundreds digit is four times the units digit. Also, the sum of its digit is 16. Find the number.

Solution :-

Let units digit be 'x'.

Thus tens = 3x

hundreds = 4x

Thus as given,

hundreds+tens+units = 16

3x+4x+x = 16

8 x = 16

units equals to 2

tens equals 3 x 2=6

hundreds equals 4x2=8

number is equal to $\rm \red{862}$

Hence Verified :)