Question

# The sum of three numbers is $$98$$. If the ratio of the first to second is $$2 :3$$ and that of the second to the third is $$5 : 8$$, then the second number is:

Solution

## Let the three parts be A, B, C. Then, $$A: B = 2:3$$ and $$B : C = 5: 8 =$$ $$\left ( 5 \times \dfrac{3}{5} \right ) : \left ( 8 \times \dfrac{3}{5} \right ) = 3: \dfrac{24}{5}$$$$=> A:B: C = 2:3:$$ $$\dfrac{24}{5}$$ $$= 10:15:24$$$$=> B =$$$$\left ( 98 \times \dfrac{15}{49} \right )$$$$=30$$Mathematics

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