Question

50 and 67 should be divided by which number so that remainder are 5 and 7 respectively ​

Answer 1

Answer:

15

Step-by-step explanation:

$Q_1, Q_2$ are quotients.

(A) 50 ÷ $x$ = $Q_1$ ... 5

(B) 67 ÷ $x$ = $Q_2$ ... 7

Rewrite (A) and (B)

$xQ_1+5=45$

$xQ_2+7=67$

$xQ_1=45, xQ_2=60$

45 and 60 are divided without remainder by x.

Common factor of 45 and 60 are the factors of 15.

(Highest common factor is 15.)

$1,3,5,15$ are the factors of 15.

Remainder should be greater than 0 or equal and less than x.

Remember : 0≤(Remainder)<x

1, 3, 5 are less than 7, which is the remainder of (B).

1, 3, 5 can't be x.

∴$x=15$

If you try dividing it, you can see that the remainder is 5 and 7.