CAT 2022 Slot 1 Paper

Question : 48 of 66

Marks: +1, -0

Let $0 ≤ a ≤ x ≤ 100$ and $f(x)=|x-a|+|x-100|+|x-a-50|$ .Then the maximum value of f(x) becomes 100when a is equal to

Solution:

x>=a, \;\text " so "\;|x-a|=x-a

x< 100, \;\text " so "\;|x-100|=100-x

f(x)=(x-a)+(100-x)+|x-a-50|=100

or,

|x-a-50|=a

From the graph we can can see that when

{\x}= {\a}

then

|x-a-50|=a

or,

a=50

Similarly when

{x}= {a}+100

|x-a-50|=a

or,

a=50

So value of a is 50 when

f(x)

is 100 .

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