Question

A number when divided by the sum of \[\;555\] and \[445\] gives two times their difference as quotient and \[30\] as the remainder. The number is

Answer 1

Hint:First we consider the number as N.Here we use a simple division method, Add the remainder with the product of divisor and quotient.Divided by the sum of two number gives two times their difference is represents as a quotient and also that the remainder was \[30\].Then we find that number.


Complete step-by-step answer:
It is given that the number divided by the sum of \[\;555\] and \[445\] gives two times their difference as
Quotient and remainder is \[30\]
Let us consider the number be N
Now we find the quotient, but we have an given was N is divided by the sum of 555 and 445,
The quotient is 2 times difference at the sum of the \[\;555\] and \[445\].
That is we can write in the form of,
Quotient = two times their difference
Quotient \[ = 2\left( {555 - 445} \right) = 220\]
Divisor \[ = {\text{ }}555 + 445 = 1000\]
Also the remainder is \[30\]
Already we know that, add reminder with the product of divisor and quotient i.e
\[\text{Number} = \text{Divisor} \times \text{quotient} + \text{Remainder}\]
Number \[ = 1000 \times 220 + 30\]
On simplifying we get,
Number \[ = 220030\]
Therefore the number, \[N = 220030\]
The number, when divided the sum of \[\;555\] and \[445\] gives two times their difference as
quotient and \[30\] as the remainder.
Hence, the number is \[\;220030\] and the quotient is \[220\] and the divisor is \[1000\].

Note:The number which we divide is called the dividend. The number by which we divide is called the divisor. The result obtained is called the quotient. The number left over is called the remainder.Also students should remember the formula i.e.\[\text{Number} = \text{Divisor} \times \text{quotient} + \text{Remainder}\] for solving these types of questions.