S.chand books class 8 maths solution chapter 10 Direct and Inverse variation exercise 10 C

EXERCISE 10 C

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Q1 | Ex-10C | Class 8 | Direct and inverse variation | SChand Composite Maths | myhelper
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Question 1

4 mens can make 4 cupboards in 4 days ; how many cupboards can 14 mens make in 14 days ?

Sol :

As number of men ∝ number of cupboards or Number of days

In 4 days 4 mens make 4 cupboards

∴ In 1 day 4 mens make $\dfrac{4}{4}$ cupboards [dividing 4 both sides]

∴ In 1 day 1 men make $\dfrac{4}{4\times 4}$ cupboards [dividing 4 both sides]

∴ In 1 day 14 mens make $\dfrac{4}{4\times 4}\times 14$ cupboards [multiplying 14 both sides]

∴ In 14 days 14 mens make $\dfrac{4}{4\times 4}\times 14 \times 14$ cupboards [multiplying 14 both sides]

$=\dfrac{4}{16}\times 14 \times 14$

= 49 cupboards

 

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Q2 | Ex-10C | Class 8 | Direct and inverse variation | SChand Composite Maths | myhelper
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Question 2

In a hostel it costs 1800 to keep 50 students for 8 weeks . For what length of time did the cost of keeping 90 students amount to 21060

Sol :

As cost ∝  Student or weeks

⇒To keep 50 students for 8 weeks it costs 1800

⇒To keep 50 students for 1 weeks it costs $\dfrac{1800}{8}$ [Dividing 8 both sides]

⇒To keep 1 students for 1 weeks it costs $\dfrac{1800}{8\times 50}$ [Dividing 50 both sides]

⇒To keep 90 students for 1 weeks it costs $\dfrac{1800}{8\times 50}\times 90$ = 405 [Multiplying 90 both sides]

⇒So with amount 21060 ,  90 students stay $\dfrac{21060}{405}=52$ weeks

 

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Q3 | Ex-10C | Class 8 | Direct and inverse variation | SChand Composite Maths | myhelper
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Question 3

39 persons can repair a road in 12 days working 5 hours per day . In how many days will 30 persons working 6 hours per day complete the work ?

Sol :

$\text{Number of persons} \propto \dfrac{1}{\text{Number of working days}}$

Case 1:

39 persons working 5 hours per day to repair a road take 12 days which is equal to 2340

⇒39×5×12 = 2340..(i)

Case 2:

30 persons working 6 hours per day to repair a road take x days which is equal to 180x

⇒30×6 = 180x ..(ii)

From (i) and (ii) , we get

⇒2340 = 180x

⇒$x=\dfrac{2340}{180}$

⇒x = 13

⇒13 days

 

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Q4 | Ex-10C | Class 8 | Direct and inverse variation | SChand Composite Maths | myhelper
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Question 4

If 15 bottles of water are needed for seven men for two days , how many bottles are required for four mens for seven days ?

Sol :

Number of bottles ∝ Number of mens

⇒7 mens for 2 days need 15 bottles

⇒7 mens for 1 days need $\dfrac{15}{2}$ bottles [Dividing 2 both sides]

⇒1 men for 1 day need $\dfrac{15}{2\times 7}$ bottles [Dividing 7 both sides]

⇒1 men for 7 days need $\dfrac{15}{2\times 7}\times 7$ bottles [Multiplying 7 both sides]

⇒4 mens for 7 days need $\dfrac{15}{2\times 7}\times 7\times 4$ bottles  [Multiplying 7 both sides]

⇒30 bottles are needed

 

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Q5 | Ex-10C | Class 8 | Direct and inverse variation | SChand Composite Maths | myhelper
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Question 5

10 cooks working for 8 hours each can prepare a meal for 536 people . How many cooks will be needed to prepare a meal for 737 people , if they are required to prepare a meal in 5 hours ?

Sol :

As cooks ∝ meal for peoples

⇒10 cooks working 8 hours to prepare meal for 536 peoples

⇒If 10 cooks work 1 hour, then they prepare meal for $\dfrac{536}{8}$ peoples

⇒If 1 cooks work 1 hour, then it prepare meal for $\dfrac{536}{8\times 10}$ peoples

⇒If 1 cooks work 5 hour, then it prepare meal for $\dfrac{536}{8\times 10}\times 5$ peoples = 33.5 ..(i)

⇒If we have to prepare meal for 737 people then cooks required is equal to

$=\dfrac{737}{33.5}$ [from (i)]

= 22 cooks

 

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Question 6

A garrison of 1200 men has sufficient rations for 25 days at the rate of 2400 g per man per day . If 300 men join them and the rations are reduced to 2000 g per man per day , how long will the food last all of them ?

Sol :

$\text{Number of men}\propto\dfrac{1}{\text{Number of Days}}$

Case 1:

⇒Total men 1200 has ration for 25 days at rate of 2400 g per man per day which is equal to 72000000

⇒1200×25×2400=72000000..(i)

Case 2:

⇒Total men 1200+300=1500 has ration for x days at rate of 2000 g per man per day which is equal to 3000000

⇒1500×x×2000 = 3000000x..(ii)

On dividing  (i) by (ii) , we get number of days ration last for 1500 peoples at rate of 2000 g per man per day

⇒$x=\dfrac{72000000}{3000000}$

x = 24

24 days

 

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Question 7

If a man travels 65 km in 3 days by walking $7\dfrac{1}{2}$ hours a day , in how many days will he travel 156 km by walking 8 hours a day ?

Sol :

Case 1 :

⇒In 3 days a man walk $7\dfrac{1}{2}$ hours a day to cover 65 km

⇒In 3 days a man walk $\dfrac{15}{2}$ hours a day to cover 65 km

⇒In 1 days a man walk $\dfrac{15}{2}$ hours a day to cover $\dfrac{65}{3}$ km

⇒In 1 days a man walk 1 hour a day to cover $\dfrac{65}{3}\times \dfrac{2}{15}$ km

⇒In 1 days a man walk 8 hours a day to cover $\dfrac{65}{3}\times \dfrac{2}{15}\times 8$ km

⇒In x days a man walk 8 hours a day to cover $\dfrac{65}{3}\times \dfrac{2}{15}\times 8\times x$ km or $\dfrac{13}{3}\times \dfrac{2}{3}\times 8\times x$ or $\dfrac{208x}{9}$ km ..(i)

Case 2:

In x days a man walks 8 hours a day cover 156 km ..(ii)

Equation (ii) must be equal to (i)

⇒$\dfrac{208x}{9}=156$

⇒$x=\dfrac{156\times 9}{208}$

$=\dfrac{78\times 9}{104}=\dfrac{39\times 9}{52}$

$=\dfrac{351}{52}=\dfrac{27}{13}$

$=6\dfrac{3}{4}$ days

 

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