### If m+n =24, then (m-16)^{3} + (n-8)^{3} is ?

**Options : **

a) 0

b) 320

c) 576

d) 40

SSC CGL Paper 2024 : Quantitative Aptitude

### Solution :

m+n =24,

=> m=24-n

Put value of m in equation : (m-16)^{3} + (n-8)^{3}

=> (24-n-16)^{3} + (n-8)^{3}

=> (8-n)^{3} + (n-8)^{3}

=> (8-n)^{3} + (n-8)^{3}

=> -(n-8)^{3} + (n-8)^{3}

=> (n-8)^{3} (-1+1)

=>(n-8)^{3} x0 = 0

Correct Answer a) 0