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Using Componendo-Dividendo, if a+ba−b=53\frac{a+b}{a-b} = \frac{5}{3}, find a:ba:b.

  1. 4:14:1

  2. 3:13:1

  3. 5:25:2

  4. 2:12:1

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Correct answer

4:14:1

Explanation

Componendo-Dividendo: (a+b)+(a−b)(a+b)−(a−b)=5+35−3⇒2a2b=82=4\frac{(a+b)+(a-b)}{(a+b)-(a-b)} = \frac{5+3}{5-3} \Rightarrow \frac{2a}{2b} = \frac{8}{2} = 4. So a/b=4a/b = 4, hence a:b=4:1a:b = 4:1.

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All 30 Ratio and proportion questions

  1. 1.What is the ratio of 20 to 25 in its simplest form?
  2. 2.If a:b = 3:4 and b:c = 8:9 , what is the compounded ratio a:b:c ?
  3. 3.What is the duplicate ratio of 2:3 ?
  4. 4.Find the mean proportional between 4 and 16.
  5. 5.If x:y = 5:7 , what is the inverse ratio of x:y ?
  6. 6.If a:b = 2:5 and c:d = 10:3 , what is the compounded ratio of a:b and c:d ?
  7. 7.What is the fourth proportional to 2, 5, 4 ?
  8. 8.If a:b = c:d and a=6, b=8, c=9 , find d using cross multiplication.
  9. 9.Given a:b = 3:2 , apply the Componendo rule to find (a+b):b .
  10. 10.What is the third proportional to 4 and 6 ?
  11. 11.The ages of A and B are in the ratio 5:7 .
  12. 12.Two numbers are in the ratio 3:5 .
  13. 13.If a:b = 2:3 , b:c = 4:5 , and c:d = 6:7 , find a:d .
  14. 14.The ratio of incomes of X and Y is 5:4 and the ratio of their expenditures is 7:5 .
  15. 15.A mixture contains milk and water in the ratio 5:3 .
  16. 16.Using Componendo-Dividendo, if a+b/a-b = 5/3 , find a:b .
  17. 17.What is the third proportional to 12 and 18 ?
  18. 18.A sum of \ 1200 is divided among A, B, and C in the ratio 2:3:5$.
  19. 19.If x/y = 4/5 , find the value of 2x+3y/3x-2y .
  20. 20.Two partners A and B invest \ 5000 and \ 8000 in a business.
  21. 21.The ratio of incomes of X and Y is 7:5 .
  22. 22.A bag contains coins of denominations \ 1 , \ 0.50 , and \ 0.25 in the ratio 3:4:5 .
  23. 23.If y varies directly as x^2 and inversely as z , and y=12 when x=2 and z=3 , find y when x=4 and z=6 .
  24. 24.The present ages of A and B are in the ratio 5:6 .
  25. 25.A and B start a partnership with capitals of \ 8000 and \ 12000 respectively.
  26. 26.In a mixture of 60 liters, milk and water are in the ratio 2:1 .
  27. 27.A vessel contains 20 liters of pure milk.
  28. 28.A and B enter into a partnership with capitals in the ratio 3:5 .
  29. 29.If a/b = 3/4 , b/c = 5/6 , and c/d = 7/8 , find a:d .
  30. 30.A vessel contains 40 liters of a mixture of milk and water in the ratio 5:3 .