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Standard VI

Mathematics

Equivalent Ratios

If x:y=1:2,...

Question

If $x : y = 1 : 2$ , find the value of $(2 x + 3 y) : (x + 4 y)$ .

12 : 4

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3 : 13

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14 : 2

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8 : 9

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Solution

The correct option is C $8 : 9$
$x : y = 1 : 2$ means $\frac{x}{y} = \frac{1}{2}$

Now, $(2 x + 3 y) : (x + 4 y) = \frac{(2 x + 3 y)}{(x + 4 y)}$

$= \frac{\frac{2 x + 3 y}{y}}{\frac{x + 4 y}{y}}$

$= \frac{2 \frac{x}{y} + 3}{\frac{x}{y} + 4}$

Putting $\frac{x}{y} = 12$ , we get,

$= \frac{2 \cdot \frac{1}{2} + 3}{\frac{1}{2} + 4} = \frac{8}{9}$

Thus, the required ratio is $8 : 9$ .

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Similar questions

Q. 1. If

x : y = 3 : 5

,find the ratio

3 x + 4 y : 8 x + 5 y

.
2. If

x : y = 8 : 9

find the ratio

(7 x - 4 y) : 3 x + 2 y

3. If two numbers are in the ratio

6 : 13

and their l.c.m. is

312

, find the numbers.
4. What should be added to each term of the ratio

7 : 13

so that the ratio becomes

2 : 3

Q. The following are the steps involved in finding the value of X : y , if

\frac{3 x + 4 y}{2 x + 5 y} = \frac{4}{3}

.
Arrange them in sequential order from the first to the last.
1)

9 x + 12 y = 8 x + 20 y

2) Given

\frac{3 x + 4 y}{2 x + 5 y} = \frac{4}{3}

\frac{x}{y} = 8 \Rightarrow x : y = 8 : 1

3 (3 x + 4 y) = 4 (2 x + 5 y)

x = 8 y

Q. Find the value of each of the following:
(i)

{(\frac{1}{2})}^{- 1} + {(\frac{1}{3})}^{- 1} + {(\frac{1}{4})}^{- 1}

(ii)

{(\frac{1}{2})}^{- 2} + {(\frac{1}{3})}^{- 2} + {(\frac{1}{4})}^{- 2}

(iii) (2⁻¹ × 4⁻¹) ÷ 2⁻²
(iv) (5⁻¹ × 2⁻¹) ÷ 6⁻¹

Prove that:
(i) $\frac{1}{3 + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + 1} = 1$
(ii) $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}} = 2$

Add
$t - t^{2} - 14$ , $15 t^{3} + 13 + 9 t - 8 t^{2}$ , $12 t^{2} - 19 - 24 t$ and $4 t - 9 t^{2} + 19 t^{3}$ .

If $t = - 1$ find the value of the expression. [4 MARKS]

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If x:y=1:2, find the value of (2x+3y):(x+4y).

The correct option is C 8:9x:y=1:2 means xy=12Now, (2x+3y):(x+4y)=(2x+3y)(x+4y)=2x+3yyx+4yy=2xy+3xy+4Putting xy=12, we get,=2⋅12+312+4=89Thus, the required ratio is 8:9.

If $x : y = 1 : 2$ , find the value of $(2 x + 3 y) : (x + 4 y)$ .