Question

A number was divided successively in order by 4, 5 and 6. The remainders were respectively 2, 3 and 4. Find out the number lines.

Answer 1

Hint:Here we had to first assume the number which was divided in successively order. And here we also have to keep in mind that divisor * a quotient + remainder will always give us a dividend.

Complete step-by-step answer:
Let us first of all assume that the number which is dividing in successively order is ‘x’.
Now let us assume that the quotient we get on dividing ‘x’ by 4 as ‘a’.
So \[x \div 4 = a\]
And when this ‘x’ is divided by 4 we will get 2 as a remainder.
Now taking the quotient ( a ) as a dividend and again assuming ‘b’ as a quotient for the next division.
\[ \Rightarrow \]\[a \div 5 = b\], and this time we will get 3 as a remainder.
Similarly now ‘b’ will be the dividend and let the quotient be ‘c’.
\[ \Rightarrow \]\[b \div 6 = c\] and this time we will get 4 as a remainder.
Now as we all know that divisor * quotient + remainder = dividend.
So with the help of this we will get the values x, a and b.
Now first of all find the value of b.
\[ \Rightarrow \]b = 6c + 4
\[ \Rightarrow \]a = 5b + 3
Now putting the value ‘b’ in above equation
\[ \Rightarrow \]a = 5( 6c + 4 ) + 3 = 30c + 23
And x = 4a + 2
Now putting the value of ‘a’ in above equation
\[ \Rightarrow \]x = 4( 30c + 23 ) + 2 = 120c + 94
Now let us assume that the quotient ‘c’ is equal to 1.
So, x = ( \[120 \times 1\]) + 94 = 214
Hence the number is 214.

Note :- We all know that when the quotient of the dividend is taken and used as the dividend in the next division such type of division is known as successive division. So, whenever we come up with this type of problem we have to assume the dividend of the first division and the quotients we get by successive divisions. And with all these assumptions and further solving we will find the result more quickly and accurately.