Q1. There are 2 numbers. If 4 times the larger of 2 numbers is divided by the smaller one, the quotient will be 8 and the remainder will be 0. If 6 times the smaller of the 2 numbers is divided by the larger number the quotient is 3 and the remainder is 0. What are the numbers. Please give proper steps and reasons.
Answers
Answer:
let the smaller number be x and larger number be y.
condition 1
4y = 8x + 0
4y = 8x
y = 2x .......(1)
condition 2
6x = 3y + 0
6x = 3y
2x = y, or
y = 2x...........(2)
we see that (1) = (2)
Hence, we can see that with the given information we could find only one equation with two variables. Hence, we cannot find a unique solution of this problem. However, there are infinite many solutions (x,y) which satisfy the equation y = 2x like (1,2), (2,4), (3,6), (4,8),........(100,200),......(1000,2000),,,and so on.
Answer:
ANSWER
Let the larger number be x and the smaller one be y. We know that
Dividend =(Divisor × Quotient) +Remainder. (i)
When 3x is divided by y, we get 4 as quotient and 3 as remainder. Therefore, by using (i), we get
3x=4y+3⇒3x−4y−3=0 (ii)
When 7y is divided by x, we get 5 as quotient and 1 as remainder. Therefore, by using (i), we get
7y=5x+1⇒5x−7y+1=0 .(iii)
Solving equations (ii) and (iii), by cross-multiplication, we get
−4−21x=3+15−y=−21+201
−25x=−1, 18−y=−1
⇒x=25 and y=18
Hence, the required numbers are 25 and 18.