Question

If true then enter $1$ and if false then enter $0$

Dividing Rs.5,680 among A, B and C so that A : B = 5 : 6 and B : C = 8 : 9 the

division among A,B and C is Rs.1,600; Rs.1,920 and Rs.2,160 respectively.

Answer 1

In the given ratios "B" is the common term, and the values of B in both ratios are not equal.

To make them equal, find the L.C.M. of values corresponding to B i.e., $6$ and $8$.

L.C.M. of $6$ and $8=24$
Therefore, an equivalent ratio of $A:B$ such that $B=24$ $=5:6=5\times 4:6\times 4=20:24$

Similarly, an equivalent ratio of $B:C=8:9=8\times 3:9\times 3=24:27$

Therefore,$A:B:C=20:24:27$

Let the parts be $A=20x,B=24x,C=27x$

$=>20x+24x+27x=Rs5680$

$71x=Rs5680$

$x=Rs80$

$=>A=20\times Rs80=Rs1600$
$B=24\times Rs80=Rs1920$
$C=27\times Rs80=Rs2160$