Concise Mathematics>Chapter 7 - Ratio and Proportion (Including Properties and Uses)>EXERCISE>Q 9

HARD

10th ICSE

IMPORTANT

Earn 100

Find the third proportional to $a^{2} - b^{2}$ and $a + b$ .

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Important Questions on Ratio and Proportion (Including Properties and Uses)

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 7 - Ratio and Proportion (Including Properties and Uses)>EXERCISE>Q 9

Find the mean proportion to $(x - y)$ and $(x^{3} - x^{2} y)$ .

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 7 - Ratio and Proportion (Including Properties and Uses)>EXERCISE>Q 10

Find two numbers such that the mean proportional between them is

14

and third proportional to them is

112

.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 7 - Ratio and Proportion (Including Properties and Uses)>EXERCISE>Q 11

If

x

and

y

be unequal and

x : y

is the duplicate ratio of

x + z

and

y + z

, prove that

z

is mean proportional between

x

and

y

.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 7 - Ratio and Proportion (Including Properties and Uses)>EXERCISE>Q 12

If

x = \frac{2 a b}{a + b},

find the values of:

\frac{x + a}{x - a} + \frac{x + b}{x - b} .

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 7 - Ratio and Proportion (Including Properties and Uses)>EXERCISE>Q 13

If

(4 a + 9 b) (4 c - 9 d) = (4 a - 9 b) (4 c + 9 d),

prove that:

a : b = c : d .

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 7 - Ratio and Proportion (Including Properties and Uses)>EXERCISE>Q 14

If $\frac{a}{b} = \frac{c}{d},$ show that :

$(a + b) : (c + d) = \sqrt{a^{2} + b^{2}} : \sqrt{c^{2} + d^{2}}$ .

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 7 - Ratio and Proportion (Including Properties and Uses)>EXERCISE>Q 15

There are

36

members in a student council in a school and the ratio of the number of boys to the number of girls is

3 : 1

. How many more girls should be added to the council so that the ratio of number of boys to the number of girls may be

9 : 5

?

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 7 - Ratio and Proportion (Including Properties and Uses)>EXERCISE>Q 16

If $7 x - 15 y = 4 x + y$ , find the value of $x : y$ . Hence, use componendo and dividendo to find the value of $\frac{9 x + 5 y}{9 x - 5 y}$ .