Simplify the given expression.

$\frac{[120\times120\times120-100\times100\times100]}{[120\times120+120\times100+100\times100]}$

A, B and C can do a piece of work in 20, 30 and 60 days, respectively. In how many days can A do the work if he is assisted by both B and C on every third day?

Soham’s initial expenditure and savings were in the ratio of 5 ∶ 3. His income increases by 25%. If his initial savings were ₹4,500, find his income (in ₹) after the increment.

If (a + b + c) = 14, and (a³ + b³ + c³ - 3abc) = 98, find the value of (a² + b² + c²).