# Moderate Number System Solved QuestionAptitude Discussion

 Q. A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
 ✖ A. 13 ✖ B. 59 ✖ C. 35 ✔ D. 37

Solution:
Option(D) is correct

Let the original number be '$a$'
Let the divisor be '$d$'

Let the quotient of the division of $a$ by $d$ be '$x$'

Therefore, we can write the relation as $a/d = x$ and the remainder is 24.
i.e., $a = dx + 24$

When twice the original number is divided by $d, 2a$ is divided by $d$.
We know that $a = dx + 24$. Therefore, $2a = 2dx + 48$

The problem states that  $(2dx + 48)/d$ leaves a remainder of 11.

$2dx$ is perfectly divisible by $d$ and will, therefore, not leave a remainder.

The remainder of 11 was obtained by dividing 48 by $d$.

When 48 is divided by 37, the remainder that one will obtain is 11.

Hence, the divisor is 37.

Edit: For an alternative solution using equations check comment by Selvarathi.

Edit 2: For a  short alternative solution, check comment by Jamuna.

Edit 3: For yet another alternative solution, check comment by Shahetha.

Edit 4: For yet another quick alternative solution, check comment by Shobia.

Edit 5: For an alternative solution involving modular arithmetic, check comment by Sanjay Mohan Bhatnagar.

## (10) Comment(s)

Sanjay Mohan Bhatnagar
()

I shall do it using modular arithmetic.

Given for some number P which is divisible by N, remainder is 24.

P = 24 mod N

Hence, 2P = 48 mod N .......................... (1)

Further given, 2P = 11 mod N .......................... (2)

Since 48 - 11 = 37, the remainder is 37.

Sanjay Mohan Bhatnagar
()

Sorry, not remainder, rather divisor is 37. Typing mistake.

Ranjeet
()

this website is very lose man very very lose

Xyz
()

How do u manage to post such preposterous solution..!! huh... challenge ur intelligence..

Shobia
()

i) $24-11=13$

ii) $24+13=37$

so Ans: $37$

Shahetha
()

let number be, $x$

divisor be, $y$

$x \div y=24\rightarrow1$
- - -
$2x \div y=11 \rightarrow 2\\ =-1x=13\\ x=-13 \rightarrow 3$

substitute 3 in 1/2
$x\div y=24\\ -13\div y=24\\ y=24 +13\\ y=37$

PRATYUSH ANAND
()

Hi 2 All,

consider original number

as dividened is 41

divisor as 13

then do the divison as per the problem suggest.

and for solving apply the formula given by admin or friends whatever you suggest. It does not work.

Jamuna
()

twice the remainder $24*2=48$

$48-11=37$

Nagaraju
()

perfect logic

Selvarathi
()

$2a-2dx=48$

$2a-dx=11$

By solving these 2 equation we can get the answer $x=37.$