10th Class Maths NCERT Online Solutions- Real Numbers

Few Solved examples for Maths Class 10th students

NCERT Maths Solutions Class 10

Eg 1-A number, when divided by 53, gives 34 as quotient and 21 as remainder. Find the number.

Soln-Using Euclid’s division algorithm we have

Dividend= (divisor*quotient) +remainder

= (53*34) +21

= (1802+21)

=1823

NCERT Maths Solutions Class 10

Eg 2 – Show that one and only one out of n, (n+1) and (n+2) is divisible by 3, where n is any positive integer?

Sol – let’s assume that on dividing n by 3, q will be the quotient and r will be the remainder.

N=3q+r where r=0, 1 or 2

N=3q or n =3q+1 or n 3q+2

Case 1 – if n=3q, then n is clearly divisible by 3.

Case 2 – if n= (3q+1), then (n+2)=3q+3=3(q+1),which is clearly divisible by 3,hence (n+2) is divisible by 3

Case 3 – if n= (3q+2), then (n+1)=(3q+3)=3(q+1),which is clearly divisible by 3,hence (n+1) is divisible by 3

Hence only one out of 3 is divisible by 3.

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