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

please answer in full explanation

Answer 1

let the original number be A.let the divisor be D.let the quotient of dividing a by d be x.therefore ,we can write the divisor as x and the remainder is 24.i.e. a= dx +24.twice the original number is divided by d means 2a is divided by d. we know that a =dx+24. therefore, 2a = 2 (dx +48) is divided by d the remainder is 11. 2dx is divisible by d and will therefore, not leave a remainder. the remainder of 11 would be the remainder of dividing 48 by d. the question is "what number will leave a remainder of 11 when it divides 48 "?when 37 divides 48 ,the remainder 11. hence the divisor is 37.

Answer 2

Ohk So Let the divisor be x and quotient be y. 

Then, number = xy + 24......(1) 

Twice the number = 2xy + 48......(2)

So Now, 2xy is completely divisible by x. 

But On dividing 48 by x remainder is x. 

Therefore x = 48-11 = 37

Hence the answer is D 37