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Mathematics

If a sum of ₹ x is divided between A and B in the ratio ab:cd\dfrac{a}{b} : \dfrac{c}{d}, then A gets:

  1. ₹(abxac+bd)\Big(\dfrac{abx}{ac + bd}\Big)

  2. ₹(abxad+bc)\Big(\dfrac{abx}{ad + bc}\Big)

  3. ₹(adxad+bc)\Big(\dfrac{adx}{ad + bc}\Big)

  4. ₹(adxab+cd)\Big(\dfrac{adx}{ab + cd}\Big)

Ratio Proportion

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Answer

The sum ₹ x is divided between A and B in the ratio :

A : B = ab:cd\dfrac{a}{b}:\dfrac{c}{d}

L.C.M of denominators bd:

A : B = ab×bd:cd×bd\dfrac{a}{b} \times bd :\dfrac{c}{d} \times bd

A : B = ad : bc

Sum of the ratio = ad + bc.

The sum of money A get = adad+bc×x=adxad+bc\dfrac{ad}{ad + bc} \times x = \dfrac{adx}{ad + bc}.

Hence, option 3 is the correct option.

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