On Simplification $\frac{1}{1+z^{a-b}+z^{a-c}} + \frac{1}{1+z^{b-c}+z^{b-a}} + \frac{1}{1+z^{c-a}+z^{c-b}}$ would reduces to

$3x-2:5x+6$ the duplicate ratio of $2:3$ then find the value $x$.

The ratio of two numbers are $3:4$. The difference of their squares is $28$ greater is:

The price of scooter and moped are in the ratio $7:9$. The price of moped is $₹1,600$ more than that of scooter. Then the price of moped is:

If $A:B=3:7$, then $3a+2b:4a+5b=?$

The ratio of number of boys and the number of girls in a school is found to be $15:32$. How many boys and equal number of girls should be added to bring the ratio to $1:2$?

In a certain business A and B received profit in certain ratio B and C received profits in the same ratio. If A gets $₹1600$ and C gets $₹2500$ then how much does B get?