Question

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

Answer 1

Hint: First we will assume some as a number then we will take d as divisor then we will write the standard equation. Now in the given standard equation, we will replace the respective assumed value. We are given two statements so we will get two-equations and we have two unknowns. Hence we can solve two equations to get the values of two unknowns. And finally, we will find the values of unknowns.

Complete step-by-step answer:
Let ‘x’ be the number which is 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.
So let us assume d as the divisor. So divisor is a number by which another number is to be divided. Or a number that divides into another without a remainder.
So now we have ‘d’ as the divisor and ‘x’ as the number. By taking this, we will form an equation.
So we have our standard equation that is dividend = divisor × quotient + remainder
Hence now first we will write the equation for the given numbers.
So dividend(x)=divisor(d) x quotient (m) +remainder (24)
So this also can be written as x=md+24 ------(i)
Then we have another statement given that When twice the original number is divided by the same divisor the remainder is 11.
So we have 2x=nd+11 ----(ii)
Hence we have twice the equation (i) as equation(ii)
So now we have $ 2(md + 24) = nd + 11 $
 $ \Rightarrow 2md + 48 = nd + 11 $
 $ \Rightarrow 2md - nd = 11 - 48 $
 $ \Rightarrow d(2m - n) = - 37 $
 $ \Rightarrow d(n - 2m) = 37 $
 $ \Rightarrow d = \dfrac{{37}}{{n - 2m}} $
Hence, we have an answer as option D that is 37.
So, the correct answer is “Option D”.

Note: When we are putting the values in the standard equation we should take care of all the calculations and check if the correct values are taken in the correct positions. This will result in accuracy in answer else any misrepresentation of values will result in completely wrong results.