Question

A number when divided by a divisor leaves a remainder of 24, when twice the original number of divided by the same divisor the remainder is 11, then divisor is-

• A. 13
• B. 59
• C. 35
• D. 37

Answer 1

Answer: (D)

37

$x=m.n+24$

$2x=m.p+11$

$\Rightarrow$ $mp+11=2mn+48$

$\Rightarrow$ $mp=2mn+37$

$\Rightarrow$ $m(p-2n)=37$

$\therefore$ $m=\frac{37}{p-2n}$

$\therefore$ $37$ is prime number & $m$ is integer.

$\therefore$ $m=37$ or $1$

$\therefore$ $m=37$ [D]