 # ML Aggarwal Solutions Class 9 Mathematics Solutions for Problems on Simultaneous Linear Equations Exercise 6 in Chapter 6 - Problems on Simultaneous Linear Equations

Question 28 Problems on Simultaneous Linear Equations Exercise 6

A number of three digits has a hundred digits 4 times the unit digit and the sum of three

digits are 14. If the three digits are written in the reverse order, the value of the number is

decreased by 594. Find the number.

Let’s consider the digit at tens place as x

And let the digit at unit place be y

Then, the digit at hundred place = 4y

Hence, the number is 100 x 4y + 10 × x + y × 1 = 400y + 10x + y = 401y + 10x

So, reversing the number = 100 × y + 10 × x + 4y × 1 = 100y + 10x + 4y = 104y + 10x

Then according to the first condition given in the problem, we have

x + y + 4y = 14

x + 5y = 14 … (i)

And according to the second condition given in the problem, we have

401y + 10x = 104y + 10x + 594

401y – 104y = 594

297y = 594

y = 594/297

y = 2

On substituting the value of y in equation (i), we have

x + 5(2) = 14

x + 10 = 14

x = 14 – 10

x = 4

Therefore, the number is = 10x + 401y = 10(4) + 401(2) = 40 + 802 = 842.

Video transcript
"hi guys welcome to lido q a video i am vinit your leader tutor bringing you this question on your screen a number of three digits has a hundredth digit four times the units digit and the sum of three digits are 14. if the digits are written in the reverse order the value of the number is decreased by 594 find the number now let the tens digit be x and the units digit be y then hundreds digit will be four y right four times the units then the number we get it as 10 x plus 401 y and the reverse will be 10 x plus 104 y now from first condition we get sum of all the three digits that is x plus y plus 4y is equal to 14. this implies x plus 5 y is equal to 40. this will be equation 1. again when the digits are reversed the number becomes less by 594 right so we can say that 10x plus 401 y this is the number minus 594 is equal to 10x plus 104 y so 10x and 10x will subtract and become zero so 401 y minus 104 y is equal to 594 therefore 297 y is equal to 594 this implies y is equal to 2 replacing y is equal to 2 in equation 1 we get x plus 5 into 2 is equal to 14 this implies x is equal to 40. therefore the number is 401 into 2 plus 10 into x so x is equal to 4 not 14. so this is equal to 802 plus 40 so this is equal to 842 isn't that easy guys if you still have a doubt please leave a comment below do like the video and subscribe to our channel i'll see you in our next video until then bye guys keep learning keep flourishing "
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