Chapter 10: Direct and Inverse Proportions

Q11Written answer

Meenakshee cycles to her school at an average speed of 12 km/h and takes 20 minutes to reach her school. If she wants to reach her school in 12 minutes, her average speed should be

(a) $\dfrac{20}{3}$ km/h

(b) 16 km/h

(c) 20 km/h

(d) 15 km/h

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Ans: Correct option is (c)

Speed = 12 km/h

Time taken = 20 minutes = $\dfrac{20}{60}$ hr = $\dfrac{1}{3}$ hr

Distance covered = S × T = 12 × $\dfrac{1}{3}$ = 4km

Speed required to cover 4 km in 12 minutes = $\left( \dfrac{4}{12} \right)\times 60$ = 20 km/hr

Q12Written answer

100 persons had food provision for 24 days. If 20 persons left the place, the provision will last for

(a) 30 days

(b) $\dfrac{96}{5}$ days

(c) 120 days

(d) 40 days

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Ans: Correct option is (a)

100 persons have food provision for = 24 days

1 person will have food provision for = $24\times 100$ = 2500 days

If 20 persons left the place, then total left = $100-20$ = 80 persons

Hence, 80 persons have food provision for = $\dfrac{2400}{80}$ = 30 days

Q13Written answer

If two quantities x and y vary directly with each other, then

(a) $\dfrac{x}{y}$ remains constant.

(b) x – y remains constant.

(c) x + y remains constant.

(d) x × y remains constant.

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Ans: Correct option is (a)

Since, in direct proportion, both x and y increase or decrease together in such a manner that the ratio of their corresponding value remains constant.i.e $\dfrac{x}{y}$ remains constant.

Q14Written answer

If two quantities p and q vary inversely with each other, then

(a) x y remains constant.

(b) p + q remains constant.

(c) p × q remains constant.

(d) p – q remains constant.

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Worked solution

Ans: Correct option is (c)

If two quantities p and q vary inversely with each other, then p x q remains constant. Since, in inverse proportion, an increase in p causes a proportional decrease in q and vice-versa, Hence $p\times q = k$ (constant).

Q15Written answer

If the distance traveled by a rickshaw in one hour is 10 km, then the distance traveled by the same rickshaw with the same speed in one minute is (a) $\dfrac{250}{9}$ m

(b) $\dfrac{500}{9}$ m

(c) 1000 m

(d) $\dfrac{500}{3}$ m

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Worked solution

Ans: Correct option is (d)

Distance traveled $= 10$ km

Time taken = 1 hr

In one minute, distance covered $=\dfrac{10}{60}$ km $=\dfrac{10\times 1000}{60}$ m= $\dfrac{500}{3}$ m

Q16Written answer

Both x and y vary directly with each other and when x is 10, y is 14, which of the following is not a possible pair of corresponding values of x and y?

(a) 25 and 35

(b) 35 and 25

(c) 35 and 49

(d) 15 and 21

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Worked solution

Ans: Correct option is (b)

$x$ and $y$ are directly proportional.

$i.e., x \propto y$

If $x = 10$ and $y = 14$, then,

$10 \propto 14$ or $5 \propto 7$

Now, if we compare,

(a) $25 \propto 35 = 5\propto 7$

(b) $35 \propto 25 = 7 \propto 5$

(c) $35 \propto 49 = 5 \propto 7$

(d) $15 \propto 21 = 5 \propto 7$

Therefore, option (b) is not a possible pair of corresponding values of x and y.

Q17Written answer

If $x = 5y$, then x and y vary ______ with each other.

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Worked solution

Ans: Given, $x = 5y$

$\Rightarrow \dfrac{x}{y} = \dfrac{5}{1} = k$

Hence x and y vary directly with each other.

Q18Written answer

If $xy = 10$, then x and y vary ______ with each other.

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Worked solution

Ans: Given, $ xy = 10$

$\Rightarrow x = \dfrac{10}{y} = k$

Hence, x and y vary Inversely with each other.

Q19Written answer

When two quantities x and y are in ______ proportion or vary ______ they are written as $x \propto y$.

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Ans: When two quantities x and y are in direct proportion or vary directly, they are written as $x \propto y$.

Q20Written answer

When two quantities x and y are in _______ proportion or vary ______ they are written as $x\propto \dfrac{1}{y}$ .

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Worked solution

Ans: When two quantities x and y are in indirect proportion or vary indirectly, they are written as $x\propto \dfrac{1}{y}$ .

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