Home
Class 10
MATHS
(a) If r^(2) = pq, show that p : q is th...

(a) If `r^(2) = pq`, show that `p : q` is the duplicate ratio of `(p + r)` : `(q + r)`.
(b) If `(p - x) : (q - x)` be the duplicate ratio of `p : q` then show that : `(1)/(p) + (1)/(q) = (1)/(r)`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • RATIO AND PROPORTION (INCLUDING PROPERTIES AND USES)

    ICSE|Exercise Exercise 7(B)|17 Videos

  • RATIO AND PROPORTION (INCLUDING PROPERTIES AND USES)

    ICSE|Exercise Exercise 7(C )|15 Videos

  • RATIO AND PROPORTION

    ICSE|Exercise MULTIPLE CHOICE QUESTION|61 Videos

  • REFLECTION

    ICSE|Exercise QUESTION|1 Videos

Similar Questions

Explore conceptually related problems

If 5^(-p)=4^(-q)=20^(r ) . Show that (1)/(p)+(1)/(q)+(1)/(r )=0

Show that (pvvq) to r -= (p to r) ^^ (q to r)

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

In figure, P Q=P R . Show that P S > P Q .

If q is the mean proportional between p and r , show that : pqr (p + q + r)^(3) = (pq + qr + pr)^(3) .

If p(q-r)x^(2) + q(r-p)x+ r(p-q) = 0 has equal roots, then show that p, q, r are in H.P.

If p,q,r be three distinct real numbers, then the value of (p+q)(q+r)(r+p), is

Given that q^2-p r ,0,\ p >0, then the value of |p q p x+q y q r q x+r y p x+q y q x+r y0| is- a. zero b. positive c. negative \ d. q^2+p r

If the pth, qth, and rth terms of an A.P. are in G.P., then the common ratio of the G.P. is a. (p r)/(q^2) b. r/p c. (q+r)/(p+q) d. (q-r)/(p-q)

In figure PS is the bisector of /_Q P R of DeltaP Q R . Prove that (Q S)/(S R)=(P Q)/(P R) .

ICSE-RATIO AND PROPORTION (INCLUDING PROPERTIES AND USES)-QUESTIONS
  1. (a) If r^(2) = pq, show that p : q is the duplicate ratio of (p + r) :...

    Text Solution

    |

  2. If (3a+2b):(5a+3b)=18:29. Find a:b.

    Text Solution

    |

  3. if a : b = 5 : 3, find (5a + 8b) : (6a - 7b).

    Text Solution

    |

  4. Two numbers are in the ratio 3 : 5. If 8 is added to each number, the ...

    Text Solution

    |

  5. (i) What quantity must be added to each term of the ratio 8 : 15 so th...

    Text Solution

    |

  6. The work done by (x - 3) men in (2x + 1) days and the work done by (2x...

    Text Solution

    |

  7. When the fare of a certain journey by an airliner was increased in the...

    Text Solution

    |

  8. In a regiment, the ratio of number of officers to the number of soldie...

    Text Solution

    |

  9. if (a)/(b + c) = (b)/(c + a) = (c)/(a + b) and a + b + c = 0: show tha...

    Text Solution

    |

  10. if (a)/(b + c) = (b)/(c + a) = (c)/(a + b) and a + b + c ne 0, show th...

    Text Solution

    |

  11. Find the compound ratio of : (i) 3a : 2b, 2m : n and 4x : 3y ...

    Text Solution

    |

  12. Find the ratio compounded of the duplicate ratio of 5 : 6, the recipro...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |