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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