ML AGGARWAL CLASS 8 CHAPTER 9 Direct and Inverse Variation Exercise 9.3

 Exercise 9.3

Question 1

Sol :

Farmer can reap a field in 10 days 

his wife can reap it in 8 days 

Farmer one day work i,e reap a field is $\frac{1}{10} .$

His wife one day work is $\frac{1}{8}$

Fasmer and wife can completed if Key work together 

i.e $\frac{1}{10}+\frac{1}{8}$

$\quad=\frac{4+5}{40}=\frac{9}{40}$

∴ Both together can complete in $\frac{40}{9}$ days

Question 2

Sol :

Since A can complete $\frac{1}{5} k$ of work in 2 days

$\therefore$ A's one day work $=\frac{1}{2}$ of $\frac{1}{5}=\frac{1}{2} \times \frac{1}

{5}=\frac{1}{10}$

Since B Can Complete $\frac{2}{3}$nd of work in 8 days

$\therefore B's$ is one day wak $=\frac{2}{3}$ of $\frac{1}{8}=\frac{2}{3} \times \frac{1}{84}=\frac{1}{12}$

One days work of A and B together  = $\frac{1}{10}+\frac{1}{12}$

$\frac{6+5}{60}=\frac{11}{60} .$

∴ A and B working together can complete the work in $\frac{60}{11}$ days

Question 3

Sol :

'A' tap can fill a tank in 20 minutes 

A tap one minutes can fill $\frac{1}{20}th$ of tank

"B" Tap can fill a tank in 12 mint

In one minute, Tap B can fill $\frac{1}{12}th$ of Tank

If both taps were opened then

In one minutes, $\operatorname{Tap} A$ and $B$ can fill $=\frac{1}{20}+\frac{1}{12}$

$=\frac{3+5}{60}$

$=\frac{8}{60}$

∴ Both A and B will fill the tank in $\frac{60}{8}$ minutes 

Question 4

Sol :

A can do a work in 6 days

B Can do a work in 8 days

A's one day work $=\frac{1}{6}$

B's one day work $=\frac{1}{8}$

One days work of A and B Together = $\frac{1}{6}+\frac{1}{8}$

$\frac{4+3}{24}=\frac{7}{24}$

∴ 2 days work of A and B together = $2 \times \frac{7}{24}=\frac{7}{12}$

∴ Remaining work = $1-\frac{7}{12}=\frac{5}{12}$

∴ The no. OF days taken by  A to finish the remaining work 

$=\frac{\text { work } to \text { be done }}{\text { A's one day work }}=\frac{5 / 12}{1 / 6}=\frac{5}{122} \times6 =\frac{5}{2}$ day

Hence , A will complete the remaining work in $\frac{5}{2}$ days

Question 5

Sol :

A can do a piece of work in 40 days 

A's one day work = $\frac{1}{40}$

He works for 8 days , he complete $8 \times \frac{1}{40}=\frac{1}{5} th$ wok

Remaining work = $1-\frac{1}{5}=\frac{4}{5}$

B finisher remaining work in 16 days 

i.e B finisher $\frac{4}{5} th$ wok in $16 \times \frac{5}{4}$ day

=20 days

$\begin{aligned} A \text { and } B \text { Can completed in } &=\frac{1}{20}+\frac{1}{40} \\ &=\frac{2+1}{40}=\frac{3}{4{0}} . \end{aligned}$

∴  It takes $\frac{40}{2}$ days if they do together.

Question 6

Sol :

A and B separately do work in 10 and 15 days 

A's one day work $=\frac{1}{10}$ days

B's one day work $=\frac{1}{15}$ days

$\begin{aligned} A \text { and } B \text { one's day wak } &=\frac{1}{10}+\frac{1}{15} \\ &=\frac{3+2}{30}=\frac{5}{30}=\frac{1}{6} . \end{aligned}$

A completed the remaining work in 5 days 

i .e $\frac{1}{2}$ of the work had completed 

Remaining half work had completed by A and B together

i.e $\frac{1}{2} \times 6=3$ days

Question 7

Sol :

1 women or 5 girks take 17 days to complete a piece

of work

Since 3 women's work = 5 girls work

1 woman's work $=\frac{5}{3}$ girl's work

$: 7$ women work $=\frac{5}{3} \times 7$ i.e $\frac{35}{3}$ gins work

∴ 7women and 11 girls work $=\frac{35}{3}+11$ i .e $\frac{68}{3}$ girls work

Since 5 girls can do work in 17 days 

∴ 1 girl can do work in $5 \times 17$ i .r 85 days 

$\frac{68}{3}$  girls can do the work in $\frac{85}{68 /3}$ days 

$\frac{83 \times 3}{68}$  

$=\frac{15}{4}$ days

Hence 7 women and 11 girls working together will complete 

the work in $\frac{15}{4}$ days

Question 8

Sol :

A's one day work $=\frac{1}{10}$

B's one day wok $=\frac{1}{15}$.

So they divide money in the ratio $\frac{1}{10}: \frac{1}{15}$

i.e $\frac{1}{10} \times 30: \frac{1}{15} \times 30$ i.e $3: su m=3+2=5$

A's share = $\frac{3}{5} \times 3500=3 \times 700=2100$

B's share : $\frac{2}{5} \times 3,500=2 \times 700=1400$

Question 9

Sol :

A's one day work $=\frac{1}{2}$

B's one day work $r \frac{1}{6}$

C's one day work $=\frac{1}{3}$.

A, B , C one's days work together =$\frac{1}{2}+\frac{1}{3}+\frac{1}{6}$

$\frac{3+2+1}{6}=\frac{6}{6}=1$

$A, B, C$ completed their work by working together in 1 day

So they divide the money in the ratio $\frac{1}{2}: \frac{1}{6}: \frac{1}{3}$

i.e 

$\begin{aligned} & \frac{1}{2} \times 6: \frac{1}{6} \times 6: \frac{1}{3} \times 6 \\=& 3: 1: 2 \end{aligned}$

Sum of these terms = 3+1+2+6 

A's share $=\frac{3}{8} \times 960=3 \times 160=480$

B's share $=\frac{1}{6} \times 960=1 \times 160=160$

C's share $=\frac{2}{6} \times 960=2 \times 160=320$

Question 10

Sol :

A and B , c together do a piece of work in 15 days 

one's days work of A,B and C together  is $\frac{1}{15}$

B's one day work $=\frac{1}{30}$

C's one day work $=\frac{1}{40}$.

A's one day work =$\frac{1}{15}-\left\{\frac{1}{30}+\frac{1}{40}\right\}$

$\frac{1}{15}-\left\{\frac{4+3}{120}\right\}$

$\frac{1}{15}-\frac{7}{120}$

$=\frac{8-7}{120}$

A's one day work = $\frac{1}{120}$

∴ A alone do the work in 120 days 

Question 11

Sol :

A's one day +B's one day + C's one day =$\frac{5}{24}$

A's one day +C's one $d a y=\frac{1}{8}$.

B's one day work 

$\begin{aligned}=& \frac{5}{24}-\frac{1}{8} \\ &=\frac{5-3}{2 4} \\ &=\frac{2}{24}=\frac{1}{12} \end{aligned}$

∴  B alone can plough field in 12 days

Question 12

Sol :

A's one day work +B' s one ofay work $=\frac{1}{10}$

B's one day work +C's is one day work $=\frac{1}{15}$

C's one day work +A's 

As one day work $=\frac{1}{12}$

2 (A's one day work + B's one days work +C's one day work)

$=\frac{1}{10}+\frac{1}{15}+\frac{1}{12}$

$=\frac{6+4+5}{60}=\frac{15}{60}-\frac{1}{4}$

A's one day work + B's one day work + C's one day work = $\frac{1}{4} \times \frac{1}{2}$

$=\frac{1}{8}$

$\therefore A, B, C together can complete in 8 days

A's one day work = $\frac{1}{8}-\frac{1}{15}$

$=\frac{15-8}{120}=\frac{7}{120}$

∴ A alone takes $\frac{120}{7}$ days

B's one day work =$\frac{1}{8}-\frac{1}{12}$

= $\frac{3-2}{24}=\frac{1}{24}$

B alone takes 24 days 

C's one day work $=\frac{1}{8}-\frac{1}{10}$

$=\frac{5-4}{40}=\frac{1}{40}$

C alone takes 40 days

Question 13

Sol :

Pipe fill a tank in 12 hour

In one hour , pipe fills $\frac{1}{12}$ of the tank

A waste pipe is left opened and filled in 16 hour

In one hour , it fills $\frac{1}{16}$ of tank

∴ portion of tank emptied by the waste pipe 

in one hour = $\frac{1}{12}-\frac{1}{16}$

=$\frac{4-3}{48}$

$=\frac{1}{48}$

∴ Waste pipe takes 48 hours to empty the tank