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If (ax + by)/a = (bx - ay)/b, then show...

If ` (ax + by)/a = (bx - ay)/b`, then show that each ratio is equal to x .

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Given that ` (ax + by)/a = (bx - ay)/b = (a^(2) x + aby + b^(2) x - aby)/(a^(2) + b^(2))` [ by addendo process ]
` = (x(a^(2)+ b^(2)))/((a^(2) + b^(2))) = x`.
` :. ` each ratio = x.
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CALCUTTA BOOK HOUSE-RATIO AND PROPORTION-EXAMPLES (Long Answer Type Questions)
  1. If a : b = b : c, then prove that (abc(a+b+c)^(3))/((ab+bc+ca)^(3)...

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  2. If a, b, c, d are in continued proportion, then prove that (b -c)^(2...

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  3. If a/b = x/y, then show that (a+b) (a^(2)+b^(2))x^(3) = (x+y)(x^(2)+y...

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  4. If x/(lm - n^(2)) = y/(mn - l^(2)) = z/(nl-m^(2)), then prove that lx ...

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  5. If x/(b + c -a) = y/(c + a - b) = z/(a + b -c), then show that (b -c...

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  6. If x/y = (a + 2)/(a - 2) , then show that (x^(2) - y^(2))/(x^(2) + ...

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  7. If x = (8ab)/(a+b) , then find the value of ((x+4a)/(x - 4a) + (x+...

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  8. If a/(q -r) = b/(r-p) = c/(p-q), then prove that a + b + c = 0 =pa+...

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  9. If (ax + by)/a = (bx - ay)/b, then show that each ratio is equal to x...

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  10. If (a+b)/(b+c) = (c +d)/(d + a) , that prove that c = a " or, " a + b...

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  11. If x/(b +c) = y/(c+a) = z/(a + b), then show that a/(y+z-x) = b/(z+...

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  12. If (x+y)/(3a-b) = (y+z)/(3b-c) = (z+x)/(3c-a), then show that (x+y+z)...

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  13. If x/a = y/b = z/c , then show that (x^(2)-yz)/(a^(2)-bc) = (y^(2)-zx...

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  14. If (a + b + c + d) : (a + b - c - d) = (a - b + c - d):(a-b-c+d), then...

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  15. If a^(2)/(b + c) = b^(2)/(c +a) = c^(2)/(a + b) = 1, then show that ...

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  16. If x^(2) : (by + cz) =y^(2) : (cz + ax) = z^(2) : (ax + by) = 1, then...

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  17. If x/(xa+yb+zc) = y/(ya+zb+xc) = z/(za+xb+yc)" and " x + y + z ne 0, ...

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  18. If a/(y+z) = b/(z + x) = c/(x+y), then prove that (a(b-c))/(y^(2)-z^...

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  19. If b/(a+b) = (a+c-b)/(b+c-a) = (a+b+c)/(2a+b+2c)("where " a + b + c n...

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  20. If x/(y+z) = y/(z+x) = z/(x + y), then prove that the value of each r...

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