This is the Important question based on Linear Equations in two Variables Chapter of R.S Aggarwal book for
ICSE & CBSE Board.
Question Number 8 Exercise 3E of RS Aggarwal Solution
Here the quotient and remainder of the n time of larger and n time of smaller of two numbers is given. you have
to find the numbers.
Deepak BoraNewbie
If three times the larger of two numbers is divided by the smaller, we get 4 as the quotient and 8 as the remainder. If five times the smaller is divided by the larger, we get 3 as the quotient and 5 as the remainder. find the numbers.
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Let the larger number be x and the smaller number be y.
Given that 3 times, the larger number is divided by smaller we get 4 as Quotient and 8 as remainder.
= > 3x = y * 4 + 8
= > 3x = 4y + 8
= > 3x – 4y = 8Â Â ——— (1)
Given that if five times the smaller is divided by larger we get 3 as Quotient and 5 as remainder.
= > 5y = 3x + 5
= > 5y – 3x = 5Â Â
= > -3x + 5y = 5Â ——— (2)
On solving (1) & (2), we get
= >Â 3x – 4y = 8
= > -3x + 5y = 5
   ——————–
       y = 13
Substitute y = 13 in (1), we get
= > 3x – 4y = 8
= > 3x – 4(13) = 8
= > 3x – 52 = 8
= > 3x = 52 + 8
= > 3x = 60
= > x = 60/3
= > x = 20.
Therefore the numbers are 20, 13.