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if `a ne b` and `a : b` is the duplicate ratio of `a + c` and `b + c`, prove that `'c'` is the mean proportional between `'a'` and `'b'`.

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ICSE-RATIO AND PROPORTION (INCLUDING PROPERTIES AND USES)-QUESTIONS
  1. Find the ratio compounded of the duplicate ratio of 5 : 6, the recipro...

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  2. Find : (i) the fourth proportional to 3, 6 and 4.5. (ii) the mean ...

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  3. Quantities a, 2, 10 and b are in continued proportion, find the values...

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  4. What number should be subtracted fram each of the numbers 23, 30, 57 a...

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  5. What should be added to each of the numbers 13, 17 and 22 so that the ...

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  6. if (a^(2) + c^(2)), (ab + cd) and (b^(2) + d^(2)) are in continued pro...

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  7. if p: q :: r, prove that p : r = p^(2): q^(2).

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  8. if a ne b and a : b is the duplicate ratio of a + c and b + c, prove t...

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  9. if a + c = mb and (1)/(b)+ (1)/(d) = (m)/(c), prove that a, b, c and d...

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  10. if q is the mean proportional between p and r, prove that : p^(2) -...

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  11. if a, b, c and d are in proportion, prove that : (i) (a-b)/(c-d)=...

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  12. 6 is the mean proportion between two numbers x and y and 48 is third p...

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  13. if (8x + l3y)/(8x - 13y) = (9)/(7), find x : y.

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  14. if a : b = e : d, show that : 3a + 2b : 3a - 2b = 3c + 2d : 3c - 2d.

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  15. if (8a - 5b)/(8c - 5d) = (8a + 5b)/(8c + 5d), prove that (a)/(b) = (c...

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  16. if p = (4xy)/(x + y), find the value of (p+2x)/(p-2x) + (p+2y)/(p-2y).

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  17. if a : b = c : d prove that : (a^(2) + ac + c^(2)) : (a^(2) - ac ...

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  18. if x, y and z are in continued proportion, prove that : x^(2) - y^...

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  19. Using the properties of proportion, solve the following equation for x...

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  20. if x = (sqrt(3a + 2b) + sqrt(3a - 2b))/(sqrt(3a + 2b) - sqrt(3a - 2b)...

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