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?

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?Solution:Let the original number be 'a'.Let the divisor be 'd'.Let the quotient of dividing 'a' by 'd' be 'x'.and the remainder is 24.∴ a = dx + 24⇒ 2a = 2(dx + 24) ⇒ 2a = 2dx + 48Twice the original number is divided by 'd' means 2a is divided by d.When (2dx + 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 essentially becomes "What number will leave a remainder of 11 when it divides 48?"When 37 divides 48, the remainder is 11.Hence, the divisor is 37.