S.chand publication New Learning Composite mathematics solution of class 8 Chapter 9 Variation Exercise 9C

 Exercise 9C

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Q1 | Ex-9C | Class 8 | S.Chand | New Learning Composite maths | Variation | myhelper

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Question 1

6 men take 12 hours to weed a certain field. How long would 9 men take to do so, if all work at the same rate?

Sol :

M₁=6 men,  D₁=12 , M₂=9

M₁.D₁=M₂.D₂

or D₂$=\frac{6\times 12}{9}$=8 hr 

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Q2 | Ex-9C | Class 8 | S.Chand | New Learning Composite maths | Variation | myhelper

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Question 2

12 men can hoe a field in 10 days. How long will 15 men take?

Sol :

M₁=12 men,  D₁=10 , M₂=15

M₁.D₁=M₂.D₂

or D₂$=\frac{12\times 10}{15}$=8 days 

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Q3 | Ex-9C | Class 8 | S.Chand | New Learning Composite maths | Variation | myhelper

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Question 3

A and B can do a piece of work in 6 and 12 days respectively. They (both) will complete the work in how many days?

Sol :

A do work in 6 days

B do work in 6 days

∴efficiency of A$=\frac{1}{6}$

∴efficiency of B$=\frac{1}{12}$

∴efficiency of (A+B)$=\frac{1}{6}+\frac{1}{12}$ $=\frac{2+1}{12}=\frac{3}{12}=\frac{1}{4}$

∴(A+B) do the work in 4 days

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Q4 | Ex-9C | Class 8 | S.Chand | New Learning Composite maths | Variation | myhelper

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Question 4

Rekha can finish a work in 18 days and Prema can do the same work in half the time taken by Rekha. Then, working together, what part of the same work they can finish in a day?

Sol :

Rekha can finish a work in 18 days

∴efficiency of rekha $=\frac{1}{18}$

Prema can do a work in $=\frac{18}{2}$=9 days 

∴efficiency of prema $=\frac{1}{9}$

∴efficiency of (Rekha + Prema)$=\frac{1}{18}+\frac{1}{9}$ $=\frac{1+2}{18}=\frac{3}{18}=\frac{1}{6}$

∴A work can done by (rekha and prema) together $\frac{1}{6}$

It take 6 days to complete work when they work together.

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Q5 | Ex-9C | Class 8 | S.Chand | New Learning Composite maths | Variation | myhelper

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Question 5

A alone can complete a work in 12 days and B alone can complete the same work in 24 days. In how many days can A and B together complete the same work?

Sol :

A can do a work =12 days

B can do a work =24 days

∴efficiency of A$=\frac{1}{12}$

∴efficiency of B$=\frac{1}{24}$

∴efficiency of (A+B)$=\frac{1}{12}+\frac{1}{24}=\frac{2+1}{24}$ $=\frac{3}{24}=\frac{1}{8}$

(A+B) do work= 8 days

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Q6 | Ex-9C | Class 8 | S.Chand | New Learning Composite maths | Variation | myhelper

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Question 6

A and B together can do a piece of work in 12 days, while B alone can finish it in 30 days. In how many days can A alone finish the work?

Sol :

(A+B) do a work=12 days

∴efficiency of (A+B)$=\frac{1}{12}$

B can do alone a work=30 days

∴efficiency of B$=\frac{1}{30}$

∴efficiency of A$=\frac{1}{12}-\frac{1}{30}=\frac{5-2}{60}$ $=\frac{3}{60}=\frac{1}{20}$

∴A can do a work alone=20 days

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Q7 | Ex-9C | Class 8 | S.Chand | New Learning Composite maths | Variation | myhelper

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Question 7

A, B and C can complete a work in 2 h. If A does the job alone in 6 h and B in 5 h, how long will it take C to finish the job alone?

Sol :

(A+B+C) can complete a work=2 h

∴A can complete a work=6 h

∴B can complete a work=5 h

∴efficiency of (A+B+C)$=\frac{1}{2}$

∴efficiency of A$=\frac{1}{6}$

∴efficiency of B$=\frac{1}{5}$

∴efficiency of C$=\frac{1}{2}-\left(\frac{1}{6}+\frac{1}{5}\right)$ $=\frac{1}{2}-\left(\frac{5+6}{30}\right)=\frac{2}{15}$

∴C can do a work $=\frac{15}{2}=7\frac{1}{2}$ hours

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Q8 | Ex-9C | Class 8 | S.Chand | New Learning Composite maths | Variation | myhelper

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Question 8

A and B can do a piece of work in 72 days. B and C can do it in 120 days. A and C can do it in 90 days. In what time can A alone do it?

Sol :

(A+B) can do a piece of work=72 days

∴(B+C) can do a piece of work=120 days

∴(A+C) can do a piece of work=90 days

∴efficiency of (A+B)+(B+C)+(A+C)$=\frac{1}{72}+\frac{1}{120}+\frac{1}{90}$

∴efficiency of 2(A+B+C)$=\frac{5+3+4}{360}=\frac{12}{360}=\frac{1}{30}$

∴efficiency of (A+B+C)$=\frac{1}{30\times 2}=\frac{1}{60}$

∴efficiency of A=efficiency of (A+B+C)-efficiency of (B+C)

$=\frac{1}{60}-\frac{1}{120}=\frac{1}{120}$

∴A can do a work 120 days

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Q9 | Ex-9C | Class 8 | S.Chand | New Learning Composite maths | Variation | myhelper

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Question 9

A can do a piece of work in 10 days and B in 20 days. They begin together but A leaves 2 days before the completion of the work. In how many days will the whole work be completed?

Sol :

A can do a work in 10 days

B can do a work in 20 days

∴efficiency of A$=\frac{1}{10}$

∴efficiency of B$=\frac{1}{20}$

Let time take be x days

∴$\frac{x-2}{10}+\frac{x}{20}=1$

$\frac{2(x-2)+x}{20}=1$

or 2x-4+x=20

3x=20+4

x=8 days

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Q10 | Ex-9C | Class 8 | S.Chand | New Learning Composite maths | Variation | myhelper

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Question 10

Piyush and Ajit together can complete a work in 3 days. They started together but after 2 days Ajit left the work. If the work is completed after 2 more days, Piyush alone can complete it in how many days?

Sol :

Efficiency of (Ajit+Piyush)$=\frac{1}{3}$ part

Work together for 2 days$=\frac{1}{3}\times 2=\frac{2}{3}$ part

Remaining $=\left(1-\frac{2}{3}\right)=\frac{3-2}{3}=\frac{1}{3}$ part

Remaining part completed by piyush in 2 days

∴Piyush's 1 day work$=\frac{1}{3}-\frac{1}{2}=\frac{1}{6}$

∴Ajit's 1 day work$=\frac{1}{3}-\frac{1}{6}=\frac{2-1}{6}=\frac{1}{6}$

∴Complete by Piyush in 6 days

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Q11 | Ex-9C | Class 8 | S.Chand | New Learning Composite maths | Variation | myhelper

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Question 11

A can complete a work in 10 days, B in 12 days and C in 15 days. all of them began the work together, but A had to leave the work after 2 days of the start and B, 3 days before the completion of the work. How long did the work last?

Sol :

Efficiency of A$=\frac{1}{10}$

Efficiency of B$=\frac{1}{12}$

Efficiency of A$=\frac{1}{15}$

∴Total unit =60

Total unit divided in

A=6 unit, B=5 units, C=4 units

∴A's 2 days work=6×2=12 unit

or $2\times \frac{1}{10}+\frac{x-3}{12}+\frac{x}{15}=1$

or $\frac{12+5x-15+4x}{60}=1$

or $x=\frac{60+3}{7}=\frac{63}{9}=7$ days

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Q12 | Ex-9C | Class 8 | S.Chand | New Learning Composite maths | Variation | myhelper

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Question 12

Sanjay and Ranbir can do a piece of work in 45 and 40 days respectively. They began the work together but Sanjay leaves after some days and Ranbir finished the remaining work in 23 days. After how many days did Sanjay leave?

Sol :

Efficiency of (Sanjay+Ranbir)$=\frac{1}{45}+\frac{1}{40}$

$=\frac{8+9}{360}=\frac{17}{360}$

∴Total work =360 {8 and 9}

Ranbir work 23 days=23×9=207 unit

∴Total work done by (Sanjay+Ranbir) together=360-207=153 units

∴Sanjay leave$=\frac{153}{8+9}=\frac{153}{17}$

=9 days