A sum of $\text{₹}x$ is divided among A, B and C such that the ratio of shares of A and B is $3:4$ and that of B and C is $5:6$. If C receives $\text{₹}1440$ more than what A receives, then the value of $x$ is?

To find the combined ratio $A:B:C$, make the value of B equal in both ratios:$A:B=3:4=(3\times 5):(4\times 5)=15:20$$B:C=5:6=(5\times 4):(6\times 4)=20:24$ Thus, the combined ratio is:
$$A:B:C=15:20:24$$
Let the shares of A, B, and C be $15k,20k,$ and $24k$ respectively.The total sum $x$ is:
$$x=15k+20k+24k=59k$$
Given that C receives $\text{₹}1440$ more than A:
$$\text{Share of C}-\text{Share of A}=1440$$
$$24k-15k=1440$$
$$9k=1440⟹k=160$$
Now, substitute $k$ to find the value of $x$:
$$x=59\times 160=9440$$