Chapter 10: Direct and Inverse Proportions

Ans: If two quantities x and y vary directly with each other, then ratio of their corresponding values remains constant.

Ans: If two quantities p and q vary inversely with each other then, product of their corresponding values remains constant.

Ans: The perimeter of a circle and its diameter vary directly with each other.

Ans: Distance traveled by car in one hour $= 48$ km

Distance traveled in one minute $=\dfrac{48}{60}$ km

Distance traveled in 12 minutes $= \left( \dfrac{48}{60} \right)\times 12 =\dfrac{48}{5} = 9.6$ km

Ans: Distance covered by auto rickshaw in 3 hours $= 36$ km

Speed $=\dfrac{36}{3} =$ 12 km/hr

If we increase the speed by 4km/hr, then the total speed becomes $= 12+4 = 16 $km/hr

Now, the time taken by auto rickshaw will be = $\dfrac{36}{16} =\dfrac{36\times 60}{16}$ = 135 min

$= 120 + 15$= 2-hour 15min

Ans: Thickness of pile of 12 cardboard sheets = 45 mm

Thickness of 1 cardboard sheet = $\dfrac{45}{12}$ mm

Hence, thickness of a pile of 240 sheets $= \left( \dfrac{45}{12} \right)\times 240$= $900$ mm$=\dfrac{900}{10}cm = 90$ cm

Ans: If $x$ varies inversely as $y$, then

$ x\times y= k$

$\Rightarrow   4\times 6= k$

$\Rightarrow $ $k=24$

Now, if $x = 3$, then $y$ is:

$y =\dfrac{k}{x} =\dfrac{24}{3} = 8$

Ans: $\dfrac{a_1}{b_1} = \dfrac{a_2}{b_2} = k$

$\Rightarrow \dfrac{a_1}{a_1} = k = $ constant

Ans: In inverse proportion

$\dfrac{a_1}{b_1} = \dfrac{a_2}{b_2} = k$

$\Rightarrow \dfrac{a_1}{a_2} = \dfrac{b_2}{b_1} = $ constant

Ans: Area occupied by 15 postal stamps = 60cm2

Area occupied by 1 postal stamp $=\dfrac{60}{15}$ = 4 cm2

Area occupied by 120 such postal stamps $= 4\times 120 =480$ cm2