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 110.

His wife one day work is 18

Fasmer and wife can completed if Key work together 

i.e 110+18

=4+540=940

∴ Both together can complete in 409 days

Question 2

Sol :
Since A can complete 15k of work in 2 days

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 

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