Question

If half of a number exceeds one-third of the number by 10, then the number is​

Answer 1

Given :-

• Half of a number exceeds one third of the number by 10.

To find :-

• The number .

Solution :-

Let the number be X

Half of the number

= 1/2 of X

= (1/2)×X

= (1×X)/2

= X/2

One third of the number

= 1/3 of X

= (1/3)×X

= (1×X)/3

= X/3

According to the given problem

1/2 of the number = 1/3 of the number + 10

=> X/2 = (X/3)+10

=> (X/2/-(X/3) = 10

LCM of 2 and 3 = 6

=> (3X-2X)/6 = 10

=> X/6 = 10

=> X = 10×6

=> X = 60

Answer :-

The required number is 60

Check :-

The number = 60

Half of 60 = 60/2 = 30

1/3 of 60 = 60/3 = 20

Half of 60 = 30 = 20+10 = 1/3 of 60 + 10

Verified the given relations in the given problem

Answer 2

$\bold{ANSWER≈}$

Given :

• Half of a number exceeds one third of

the number by 10.

To find :

• The number.

Solution :

Let the number be X

Half of the number

= 1/2 of X

= (1/2)XX

= (1xX)/2

= X/2

One third of the number

= 1/3 of X

= (1/3)XX

= (1xX)/3

=X/3

According to the given problem 1/2 of the number = 1/3 of the number +

10

=> X/2 = (X/3)+10

=> (X/2/-(X/3) = 10

LCM of 2 and 3=6

=> (3X-2X)/6 = 10

=> X/6 = 10

=> X = 10x6

=> X = 60

Answer :

The required number is 60

Check :

The number = 60

Half of 60 = 60/2 = 30

1/3 of 60 = 60/3 = 20

Half of 60 = 30 = 20+10= 1/3 of 60 + 10

Verified the given relations in the given problem