Problems based on Numbers Test 2

Question : 14 of 40

Marks: +1, -0

The sum of four numbers is 64. If you add 3 to the first number, 3 is subtracted from the second number, the third is multiplied by 3 and the fourth is divided by 3, then all the results are equal. The difference between the largest and the smallest of the original number is:

Validate

Solution:

Let the four numbers be a, b, c and d; then

a + 3 = b - 3

= 3c = d/3

Hence,

b = a + 6; c = {a+3}/3;

d=3(a+3)=3a+9

Again,

a + b + c + d = 64

⇒a+a+6+{a+3}/3+3a+9=64

⇒5a+{a+3}/3=49

⇒{16a+3}/3=49

⇒16a=147-3

∴a=144/16=9

Hence,

d - c = 3a + 9 -{a+3}/3

={8a+24}/3={8×9+24}/3

=96/3=32

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