Question

8) A number of three digits has the hundred digit 4 times the unit digit and the sum of
three digits is 14. If the three digits are written in the reverse order, the value of the
number is decreased by 594. Find the number.

A question on Problems on Simultaneous linear equations.​

Answer 1

Answer:

answer for the given problem is given

Answer 2

Given :-

Three digit number whose sum is 14

Hundred digit= 4 times unit digit

If the digits are reversed, value of numbers gets decreased by 594

To Find :-

The number.

Solution :-

Given that,

The sum of the three numbers = 14

Hundred digit= 4 times unit digit

If the digits are reversed, value of numbers gets decreased by = 594

According to the question,

Let the digit at tens place and unit place be x and y respectively.

Then,

The digit at hundred place = 4y

Hence, the number is

$\sf 100 \times 4y+10\times x+y\times 1=400y+10x+y=401y+10x$

Now, number formed by reversing the digits

$\sf 100 \times y+10 \times x+4y \times 1=100y+10x+4y=104y+10x$

According to the question, we have

$\sf x+y+4y=14$

$\sf x+5y=14 \qquad ...(1)$

And, then

$\sf 401y+10x=104y+10x+594$

$\longrightarrow \sf 401y-104y=594$

$\sf =297y=594$

$\sf =y= \dfrac{594}{297}$

$= \sf y=2$

Substituting the value of y in equation (1), we get

$\sf x+5(2)=14$

$\longrightarrow \sf x+10=14$

$\sf \longrightarrow x = 14 - 10$

$\sf =x=4$

Therefore, the number = $\sf 10x+401y=10(4)+401(2)$

$\sf =40+802=842$

Hence, the number is 842.