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 divisior is

• A. 40
• B. 45
• C. 50
• D. 55

Answer 1

The correct option is B 45

$\Rightarrow$ Let the two numbers be $a$ and $b$ and the divisor be $d$.

$\Rightarrow$ $\frac{a}{d}=35\left(Remainder\right)$ ---- ( 1 )

$\Rightarrow$ $\frac{b}{d}=30\left(Remainder\right)$ ----- ( 2 )

$\Rightarrow$ $\frac{a+b}{d}=20\left(Remainder\right)$ ----- ( 3 )

$\therefore$ $d=(\frac{a}{d}+\frac{b}{d})-\frac{a+b}{d}$ [ According to the set theory ]

$\therefore$ $d=(35+30)-20$ [ From ( 1 ), ( 2 ) and ( 3 ) ]

$\therefore$ $d=45$

$\therefore$ Required divisor is $45$