## EXERCISE 10 A

Question 1

**Given that y is directly proportional to x and y = 40 , when x = 200 . Find the value of**

**(i) y , when x = 15**

Sol: (i)

y ∝ x ⇒ , where k is the constant of variation

Given , ⇒ k =

Also ,

[given: x=15]

= 3

**(ii) x when y = 8**

Sol: (ii)

y ∝ x ⇒ , where k is the constant of variation

Given , ⇒ k =

Also , 5y = x [given: y=8]

x = 40

Question 2

**The length (in cm) stretched by a spring is directly proportional to the amount of force (in kg) applied . Given below are some observations about the force applied and the length stretched by a spring . Find the missing values in the table**

Force (in kg) | 20 | 25 | ||
---|---|---|---|---|

Length stretched(in cm) | 18 | 15 | 28 |

Sol:

As Force and Length vary directly . So is constant

∴The constant of variation

Now , ⇒ = 24

⇒

⇒

Question 3

**Priya takes 4 hours in walking a distance of 20 km . What distance would she cover in 7 hours ?**

Sol:

Distance | 20 km | |
---|---|---|

Time | 4 hours | 7 hours |

As Distance ∝ Time ⇒

So is constant

∴The constant of variation = 5

Now ,

Distance = 7×5 = 35

**ALTERNATE METHOD**

As we know

= 5 km/hr

7 hours = 7×5 km

= 35 km

Question 4

**If 15 burners consume 90 cubic metre of gas in 2 hours , how much will 9 burners consume in the same time ?**

Sol:

Gas (m^{3}) | 90 m^{3} | |
---|---|---|

Burner | 15 | 9 |

As Gas consume ∝ Burner ⇒

So is constant

∴The constant of variation = 6

Now ,

Distance = 6×9 = 54

= 54 cubic metre or 54 m^{3}

Question 5

**The railway charges 5600 to carry a certain amount of luggage for 350 km . What should the charge be carry the same amount of luggage for 425 km ?**

Sol :

Charges | 5600 | |
---|---|---|

Distance (Km) | 350 km | 425 km |

As Charges ∝ Distance ⇒

So is constant

∴The constant of variation = 16

Now ,

Distance = 16×425 = 6800

Question 6

**89 litres of oil cost 2091.50 . What is the cost of 15 litres ?**

Sol :

Oil Cost | 2091.50 | |
---|---|---|

Litres | 89 | 15 |

As Cost ∝ Litres ⇒

So is constant

∴The constant of variation = 23.50

Now ,

Cost = 23.50×15 = 352.50

Question 7

**68 packets weigh 1 kg 632 g . What will be weight of 70 packets ?**

Sol :

Weigh | 1 kg 632 g (1632g) | |
---|---|---|

Packets | 68 | 70 |

As Weigh ∝ Packets ⇒

So is constant

∴The constant of variation = 24

Now ,

Cost = 24×70 = 1680 g

1680 g = 1 kg 680 g

Question 8

**If a man working for 49 hours earns 1715 , how much will he earn working for 27 hours ?**

Sol :

Earns | 1715 | |
---|---|---|

Hours (hours) | 49 | 27 |

As Earns ∝ Hours ⇒

So is constant

∴The constant of variation = 35

Now ,

Cost = 35×27 = 945

Question 9

**The distance travelled by a ball dropped from an airplane is directly proportional to the square of time t . Given that t=2 seconds when d = 24 meters , find the distance the ball drops in 10 seconds .**

Sol:

Distance (m) | 24 m | |
---|---|---|

Time (sec) | 2 sec | 10 sec |

As Distance ∝ Time ⇒

So is constant

∴The constant of variation = 12

Now ,

Distance = 12×10 = 120

= 120 metres