Question

If two numbers, when divided by a certain divisor, give remainder $35$ and $30$ respectively and when their sum is divided by the same divisor, the remainder is $20$, then the divisor is:

• A. $40$
• B. $45$
• C. $50$
• D. $55$

Answer 1

Answer: (B)

$45$

Let the two numbers be $N_1$ and $N_2$.
$N_1$ gives a remainder of 35 when divided by some divisor $D$. Hence $N_1$ has to be 35 more than a multiple of D. In quotient remainder form we can write as $N_1=D.Q_1+35$......(1)
Similarly, $N_2$ gives a remainder of 30 when divided by the same divisor $D$. Hence $N_2$ has to be 30 more than a multiple of D. In quotient remainder form we can write as $N_2=D.Q_2+30$......(2)
where $Q_1$ and $Q_2$ are quotients.
Adding (1) and (2) we get $N_1+N_2=D(Q_1+Q_2)+65$
As per the question, the sum gives a remainder of 20 when divided by the same divisor $D$. Hence the divisor has to be 20 less than 65. (since $D(Q_1+Q_2)$ is divisible by $D$ )
So we get $D=65-20=45$