EXERCISE 2.4
Question 1
(i) Reciprocal of $\frac{3}{7}=\frac{1}{(3 / 7)}=\frac{7}{3} .$
(ii) Reciprocal of $\frac{13}{9}=\frac{1}{\left(\frac{13}{9}\right)}=\frac{9}{13}$
(iii) Reciprocal of $8=\frac{1}{8}$
Question 2
(i)
$\begin{aligned} 14 \div \frac{5}{6} &=\frac{14}{(5 / 6)} \\ &=\frac{14 \times 6}{5} \\ &=\frac{84}{5}=16 \frac{4}{5} . \end{aligned}$
(ii)
$\begin{aligned} 5 \div 3 \frac{4}{7} &=5 \div \frac{25}{7} \\ &=\frac{5}{(25 / 7)} \\ &=\frac{15 \times 7}{255} \\ &=\frac{7}{5} . \end{aligned}$
(iii)$3 \frac{1}{5} \div 1 \frac{2}{3}=\frac{16}{5} \div \frac{5}{3} .$
$=\frac{16 / 5}{5 / 3}$
$=\frac{16}{5} \times \frac{3}{5}$
$=\frac{48}{25}=1 \frac{23}{25}$
(iv)
$\begin{aligned} 2 \frac{5}{8} \div 1 \frac{1}{6} &=\frac{21}{8} \div \frac{7}{6} \\ &=\frac{21 / 8}{7 / 6} \\ &=\frac{27}{8} \times \frac{6}{7} \\ &=\frac{9}{4}=2 \frac{1}{4} . \end{aligned}$
Question 3
Total length of cloth = 7 7 $\frac{1}{2}$ metres
$=\frac{155}{2}$
Each piece of cloth length requried = $5 \frac{1}{6}$
$\frac{31}{6}$
∴ Now total no. of pieces of cloth = $\frac{155 / 2}{31 / 6}$
$\frac{155}{2} \times \frac{6}{31}$
= 15pieces
Question 4
Let the number multiplied to $4 \frac{7}{8}$ be $x$
$4 \frac{7}{8}=4+\frac{7}{8}=\frac{4 \times 8+7}{8}=\frac{32+7}{8}=\frac{39}{8}$
Required answer = $87 \frac{3}{4}$
i.e $\frac{39}{8} \times x=87+\frac{3}{4}$
$\frac{39 x}{8}=\frac{87 \times 4+3}{4}$
$\frac{39x}{8}=\frac{351}{4}$
$x=\frac{351+8}{4 \times 39}$
$x=9 \times 2$
x=18
∴ Number multiplied = 18
Question 5
Part of milk each students gets = $\frac{1}{3}$ th of Total
Total consumption of milk = $57 \frac{2}{3}$ litres
$=\frac{57 \times 3+2}{3}$
$=\frac{123}{3}$
Let the number of students in hosted b 'x '
$\frac{1}{3} \mathrm{th}$ of Total $=57 \frac{2}{3} .$
$\frac{1}{3} \times x=\frac{173}{3}$
$x=\frac{173 \times 3}{3 \times 1}$
x=173
∴ Total number of students in hostel = 173
Question 6
Given cost of $5 \frac{1}{4}$ kg apple =Rs 336
Let Cost of 1kg apples = x
$5 \frac{1}{4}=5+\frac{1}{4}=\frac{5 \times 4+1}{4}=\frac{21}{4} .$
$\begin{aligned} \frac{x}{336} &=\frac{1}{(21 / 4)} \\ \frac{x}{336} &=\frac{4}{21} \\ x &=\frac{4 \times 336}{21} \\ x &=64 \end{aligned}$
∴ Cost of apples = Rs 64 per kg
Question 7
Given area of rectangular plot = $68 \frac{3}{4} \operatorname{sq} \cdot m$
$=\frac{68 \times 4+3}{4}$
$=\frac{275}{4} \mathrm{sqm}$
Also length of rectangular plot = $12 \frac{1}{2} \mathrm{~m}$
$=\frac{12 \times 2+1}{2}$
$=\frac{25}{2} m$
We know Area of rectangle $A=$ Lensth $\times$ width
width $\times \frac{27}{2}=\frac{275}{4}$
$\quad$ width $=\frac{275 \times 2}{25 \times 4}$
$=\frac{11}{2}$
$\therefore$ Width $=5 \frac{1}{2} m$
Question 8
Given Cost of $5 \frac{1}{2}=\frac{11}{2} \mathrm{~kg}$ of sugar $=Rs 206 \frac{1}{4}$
$=\frac{206 \times 4+1}{4}$
=Rs $\frac{825}{4}$
Let Cost of $8 \frac{1}{4}=\frac{33}{4}$ Kg of sugar be 'x '
$\frac{x}{\left(\frac{825}{4}\right)}=\frac{33 / 4}{11 / 2}$
$\frac{4 x}{825}=\frac{33}{4} \times \frac{2}{11}$
$x=\frac{33}{4} \times \frac{2}{11} \times \frac{825}{4}$
$x=\frac{3 \times 825}{2 \times 4}$
$x= \frac{2425}{8}= 309 \frac{3}{8}$
∴ Cost of $8 \frac{1}{4}$ kg sugar = Rs $309 \frac{3}{8}$
Question 9
In 2 hours, Renu Completed $\frac{2}{2}$ part of work.
Let
In $1 \frac{1}{4}$ hours, Renu Completes $x^{\prime}$ past of work
1 $\frac{1}{4}=1+\frac{1}{4}=\frac{\mid x y+1}{4}=\frac{5}{y}$
i.e $\frac{x}{(2 / 3)}=\frac{5 / 4}{2}$
$x=\frac{5}{4 \times 2} \times \frac{2}{3} .$
$x=\frac{5}{12}$
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