Question
If $x : y = 3 : 4$, find $(3x + 4y) : (5x + 6y).$
✓
Answer
$\text{x : y}=3:4$
$\Rightarrow\frac{\text{x}}{\text{y}}=\frac{3}{4}$
Now $(3\text{x}+4\text{y}):(5\text{x}+6\text{y})$
$\Rightarrow\frac{3\text{x}+4\text{y}}{5\text{x}+6\text{y}}=\frac{3\frac{\text{x}}{\text{y}}+4\frac{\text{y}}{\text{y}}}{5\frac{\text{x}}{\text{y}}+6\frac{\text{y}}{\text{y}}}$ (Dividing each term by $y)$
$=\frac{3\frac{\text{x}}{\text{y}}+4}{5\frac{\text{x}}{\text{y}}+6}=\frac{3\times\frac{3}{4}+4}{5\times\frac{3}{4}+6}$
$\Big(\because\frac{\text{x}}{\text{y}}=\frac{3}{4}\Big)$
$=\frac{\frac{9}{4}+4}{\frac{15}{4}+6}=\frac{\frac{9+16}{4}}{\frac{15+24}{4}}$
$=\frac{25}{4}\times\frac{4}{39}=\frac{25}{39}$
$\therefore(3\text{x}+4\text{y}):(5\text{x}+6\text{y})=25:39$
$\Rightarrow\frac{\text{x}}{\text{y}}=\frac{3}{4}$
Now $(3\text{x}+4\text{y}):(5\text{x}+6\text{y})$
$\Rightarrow\frac{3\text{x}+4\text{y}}{5\text{x}+6\text{y}}=\frac{3\frac{\text{x}}{\text{y}}+4\frac{\text{y}}{\text{y}}}{5\frac{\text{x}}{\text{y}}+6\frac{\text{y}}{\text{y}}}$ (Dividing each term by $y)$
$=\frac{3\frac{\text{x}}{\text{y}}+4}{5\frac{\text{x}}{\text{y}}+6}=\frac{3\times\frac{3}{4}+4}{5\times\frac{3}{4}+6}$
$\Big(\because\frac{\text{x}}{\text{y}}=\frac{3}{4}\Big)$
$=\frac{\frac{9}{4}+4}{\frac{15}{4}+6}=\frac{\frac{9+16}{4}}{\frac{15+24}{4}}$
$=\frac{25}{4}\times\frac{4}{39}=\frac{25}{39}$
$\therefore(3\text{x}+4\text{y}):(5\text{x}+6\text{y})=25:39$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Explain the concept of interior and exterior angle and in the figures given below. Find $x$ and $y.$
→Observe the following data:
$a.$ Draw a bar graph to represent the above given information.
$b.$ On which day of the week was the sales maximum?
$c.$ Find the total sales during the week.
$d.$ Find the ratio of the minimum sale to the maximum sale.
$e.$ Calculate the average sale during the week.
$f.$ On how many days of the week was the sale above the average sales?
→|
Days of the week
|
Mon
|
Tues
|
Wed
|
Thurs
|
Fri
|
Sat
|
|
Number of Mobile Phone Sets Sold
|
$50$
|
$45$
|
$30$
|
$55$
|
$27$
|
$60$
|
$b.$ On which day of the week was the sales maximum?
$c.$ Find the total sales during the week.
$d.$ Find the ratio of the minimum sale to the maximum sale.
$e.$ Calculate the average sale during the week.
$f.$ On how many days of the week was the sale above the average sales?
The longer side of a parallelogram is $54\ cm$ and the corresponding altitude is $16\ cm$. If the altitude corresponding to the shorter side is $24\ cm$, find the length of the shorter side.
→Consider this data collected from a survey of a colony.
Choose an appropriate scale and draw a double bar graph. Write down your observations.
| Favourite Sport | Cricket | Basket Ball | Swimming | Hockey | Athletics |
| Watching | 1240 | 470 | 510 | 430 | 250 |
| Participating | 620 | 320 | 320 | 250 | 105 |
Choose an appropriate scale and draw a double bar graph. Write down your observations.
In Fig., $A D$ and $C F$ are respectively perpendiculars to sides $B C$ and $A B$ of $\triangle A B C$. If $\angle F C D=50^{\circ}$, find $\angle B A D$.
→Five years ago a man was seven times as old as his son. Five years hence, the father will be three times as old as his son. Find their present ages.
$ABCD$ is a quadrilateral. Is $AB + BC + CD + DA < 2(AC + BD) ?$
→Construct a $\triangle\text{ABC}$ in which $BC = 7\ cm$,$\angle\text{A}=45^\circ.$and $\angle\text{C}=75^\circ.$
→A light year is the distance that light can travel in one year.
1 light year $=9460000000000 km$
(i) Express one light year in scientific notation.
(ii) The average distance between Earth and Sun is $1.496 \times 10^8 km$. Is the distance between Earth and the Sun greater than, less than or equal to one light-year?
→1 light year $=9460000000000 km$
(i) Express one light year in scientific notation.
(ii) The average distance between Earth and Sun is $1.496 \times 10^8 km$. Is the distance between Earth and the Sun greater than, less than or equal to one light-year?
A car runs 18 km in one litre of petrol. How much distance will it cover in $3 \frac{4}{9}$ litres of petrol?
→