Question
If $a : b = 2 : 5$, find the value of $\frac{3\text{a}+2\text{b}}{4\text{a}+\text{b}}.$
✓
Answer
It is given that,
$\frac{\text{a}}{\text{b}}=\frac{2}{5}\ ....(1)$
Now,
$\frac{3\text{a}+2\text{b}}{4\text{a}+\text{b}}=\frac{(3\text{a}+2\text{b})\div\text{b}}{(4\text{a}+\text{b})\div\text{b}}$
$=\frac{3(\text{a}\div\text{b})+2}{4(\text{a}\div\text{b})+1}$
$=\frac{3\big(\frac{\text{a}}{\text{b}}\big)+2}{4\big(\frac{\text{a}}{\text{b}}\big)+1}$
$=\frac{3\big(\frac{2}{5}\big)+2}{4\big(\frac{2}{5}\big)+1}\ [\text{From (1)}]$
$=\frac{\frac{6+2\times5}{5}}{\frac{8+1\times5}{5}}$
$=\frac{6+10}{8+5}$
$=\frac{16}{13}$
$\text{Hence},\frac{3\text{a}+2\text{b}}{4\text{a}+\text{b}}=\frac{16}{13}.$
$\frac{\text{a}}{\text{b}}=\frac{2}{5}\ ....(1)$
Now,
$\frac{3\text{a}+2\text{b}}{4\text{a}+\text{b}}=\frac{(3\text{a}+2\text{b})\div\text{b}}{(4\text{a}+\text{b})\div\text{b}}$
$=\frac{3(\text{a}\div\text{b})+2}{4(\text{a}\div\text{b})+1}$
$=\frac{3\big(\frac{\text{a}}{\text{b}}\big)+2}{4\big(\frac{\text{a}}{\text{b}}\big)+1}$
$=\frac{3\big(\frac{2}{5}\big)+2}{4\big(\frac{2}{5}\big)+1}\ [\text{From (1)}]$
$=\frac{\frac{6+2\times5}{5}}{\frac{8+1\times5}{5}}$
$=\frac{6+10}{8+5}$
$=\frac{16}{13}$
$\text{Hence},\frac{3\text{a}+2\text{b}}{4\text{a}+\text{b}}=\frac{16}{13}.$
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
Replace $\square$ by the correct number: $\frac27=\;\frac8{\square}$
→What should be added to $9\frac{2}{3}$ to get $19?$
→Write the following ratios in the simplest form: $3m \ 5\ cm : 35\ cm.$
→Prove that $(5 : 6) > (3 : 4).$
→The cost price of $23 TV$ sets is $Rs. 570055$. Find the cost of each such set.
→Draw two rays $P Q$ and $R S$ as shown in Fig. (i) and (ii). Using protractor, construct angles of $15^{\circ}$ and $138^{\circ}$ with one arm $P Q$ and $R S$ respectively.
→Divide $Rs. 3450$ among $A, B$ and $C$ in the ratio $3 : 5 : 7.$
→A man can work $8$ hours daily and finishes a work in $12$ days. If he works $6$ hrs daily, in how many days will the same work be finished?
→Lines $p, q$ and $r$ are concurrent. Also, lines $p, r$ and $s$ are concurrent. Draw a figure and state whether lines $p, q, r$ and $s$ are concurrent or not.
→The following data gives the number of students of Delhi city who went abroad for study during some years:
Represent the above data with the help of a bar graph. ,
(a) Which year maximum students went to study abroad from Delhi.
(b) Which year minimum students went to study abroad from Delhi.
(c) How may total students went abroad to study between 2015 and 2017 including both the year.
(d) How may total students went abroad to study between 2014 and 2018 including both the year.
Represent the above data with the help of a bar graph. ,
(a) Which year maximum students went to study abroad from Delhi.
(b) Which year minimum students went to study abroad from Delhi.
(c) How may total students went abroad to study between 2015 and 2017 including both the year.
(d) How may total students went abroad to study between 2014 and 2018 including both the year.