**The sum of three numbers is 98. The ratio of the first to the second is ^{2}/_{3}, and the ratio of the second to the third is ^{5}/_{8}. The second number is:**

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Let the three numbers be x, y and z.

Sum of the numbers is 98.

x + y + z = 98………………(i)

The ratio of the first to the second is

^{2}/_{3}.x/y =

^{2}/_{3}.x =

^{2}/_{3}× y.x =

^{2y}/_{3}.The ratio of the second to the third is

^{5}/_{8}.^{y}/_{z}=^{5}/_{8}.^{z}/_{y}=^{8}/_{5}.z =

^{8}/_{5}× y.z =

^{8y}/_{5}.Put the value of x =

^{2y}/_{3}and z =^{8y}/_{5}in (i).^{2y}/_{3}+ y +^{8y}/_{5}= 98^{49y}/_{15}= 98.49y = 98 × 15.

49y = 1470.

y =

^{1470}/_{49}.y = 30 .

Therefore, the second number is 30