Scribd
Upload
4 views1 page

Ratio and Proportion

The document contains a series of mathematical problems related to ratios and proportions, including finding values that maintain proportional relationships among given numbers. It includes questions on mean proportionals, third proportionals, and various proofs involving ratios. The problems require algebraic manipulation and application of properties of proportions to solve for unknowns.

Uploaded by

nf42983
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
4 views1 page

Ratio and Proportion

The document contains a series of mathematical problems related to ratios and proportions, including finding values that maintain proportional relationships among given numbers. It includes questions on mean proportionals, third proportionals, and various proofs involving ratios. The problems require algebraic manipulation and application of properties of proportions to solve for unknowns.

Uploaded by

nf42983
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
You are on page 1/ 1

Ratio and proportion

Q1. What should be subtracted from each of the numbers 9, 15 and 27 so that the resulting numbers are in the
continued proportion.

Q2. If a:b = c:d then prove that:


3 a+5 b
3 c+5 d
=
√
5 ma 2+7 n b2
2
5 mc +7 n d
2

Q3. If 12 is the mean proportional between two numbers and 96 is their third proportion, find the numbers.
Q4. Find two numbers such that the mean proportional between them is 18 and their third proportional is 144.
Q5. What number must be added to each of the number 6, 15, 20 and 43 to make them proportional.
1 1 3
Q6. If p + r = 3q and + = then prove that p:q = r:s
q s r
3 2
a +3 a b 63
Q7. Given that 3 2
= , using properties of proportion find the value of a:b.
b +3 a b 62
2 a−3 b−4 c+ 5 d 2 a−3 b+4 c−5 d
Q8. If = , then prove that 5ad = 6bc.
2 a+3 b−4 c −5 d 2a+ 3 b+4 c+ 5 d

Q9. Using properties of proportion find the value of x: If


√ 3 x + 4+ √ 3 x−5 =9.
√3 x +4− √3 x−5
2 2 3 3
x + y 41 x +y
Q10. If 2 2
= , using properties of proportion find (a) x:y , (b) 3 3
x −y 40 x −y

Q11. If x= 3
√3 a+1+ √3 a−1 , then prove that x3 – 3ax2 + 3x – a = 0.
√ a+1− √3 a−1

Q12. Using properties of proportion solve for x, given


√ 5 x + √ 2 x−6 =4.
√5 x− √2 x−6
3 3
x +12 x y +27 y
Q13. Using properties of proportion, find x:y if 2
= 2
6 x +8 9 y +27
4 2 2 4 2
a + a b +b a
Q14. If b is the mean proportional between a and c, show that 4 2 2 4
= 2
b +b c +c c

Q15. If x=
√ a+3 b+ √ a−3 b
, then prove that 3bx2 – 2ax + 3b = 0.
√ a+3 b− √ a−3 b
2 2
5 x −3 x +7 2 x + 4 x−5
Q16. Using properties of proportion solve for x, If =
3 x−7 −4 x+ 5
2 2
9 a +4 a−3 5 a −7 a+2
Q17 Using properties of proportion solve for x, If = .
4 a−3 −7 a+2

You might also like