Question

the sum of one half , one third, and one fourth of a number exceed the number itself by 12 the number is​

Answer 1

The number is 144.

Step-by-step explanation:

Let, the number be, 'n'

1/2 of n = n/2

1/3 of n = n/3

1/4 of n = n/4

Hence, the sum = (n/2) + (n/3) + (n/4)

                       = (6n + 4n + 3n) /12 [∵ The L.C.M. of the denominators is 12.]

                       = 13n/12

According to the problem,

13n/12 = n+12

⇒ 13n = (n+12)×12

⇒ 13n = 12n + 144

⇒ 13n - 12n = 144

⇒ n = 144.

∴ The number is 144.

Check whether the answer is correct or wrong:

The number is 144

1/2 of 144 = 72

1/3 of 144 = 48

1/4 of 144 = 36

∴ The sum is = (72+48+36)

                     = 156

Hence, the sum exceeds the number by (156-144)

                                                                    = 12.