Question

Fill in the blanks.
(i) If 3 persons can do a piece of work in 4 days, then 4 persons can do it in ......... days.
(ii) If 5 pipes can fill tank in 144 minutes, then 6 pipes can fill it in ......... minutes.
(iii) A car covers a certain distance in 1 hr 30 minutes at 60 km per hour. If it moves at 45 km per hour, it will take ......... hours.
(iv) If 8 oranges cost Rs 20.80, the cost of 5 oranges is Rs .........
(v) The weight of 12 sheets of a paper is 50 grams. How many sheets will weigh 500 grams?

Answer 1

(i)
Let x be the number of days taken by 4 persons to complete the work.

No. of days	4	$x$
No. of persons	3	4

Clearly, more workers will take less number of days.
So, it is a case of inverse proportion.
$$\begin{gathered} \mathrm{Now},4\times 3=x\times 4 \\ \Rightarrow x=3 \end{gathered}$$
Therefore, 4 persons can do the piece of work in 3 days.

(ii)
Let x min be the time taken by 6 pipes to fill the tank.

No. of pipes	5	6
Time (in min)	144	$x$

Clearly, more number of pipes will take less time to fill the tank.
So, it is a case of inverse proportion.
$$\begin{gathered} \mathrm{Now},5\times 144=6\times x \\ \Rightarrow x=\frac{5\times 144}{6} \\ \Rightarrow x=120\min \end{gathered}$$

∴ 6 pipes can fill the tank in 120 min.

(iii)
Let x min be the time taken by the car travelling at 45 km/h.
Now, 1 h 30 min = (60+30) min

Speed(in km/hr)	60	45
Time(in min)	90	$x$

Clearly, a car travelling at a less speed will take more time.
So, it is a case of inverse proportion.
$$\begin{gathered} \mathrm{Now},60\times 90=45\times x \\ \Rightarrow x=\frac{60\times 90}{45} \\ \Rightarrow x=120\min =2\mathrm{h} \end{gathered}$$

∴ The car will take 2 h if it travels at a speed of 45 km/h.

(iv)
Let Rs x be the cost of 5 oranges.

No. of oranges	8	5
Cost of oranges	20.80	$x$

Clearly, less number of oranges will cost less.
So, it is a case of direct variation.
$$\begin{gathered} \mathrm{Now},\frac{8}{20.80}=\frac{5}{x} \\ \Rightarrow x=\frac{5\times 20.80}{8} \\ \Rightarrow x=13 \end{gathered}$$
∴ The cost of 5 oranges is Rs 13.

(v)
Let x be the number of sheets that weigh 500 g.

No. of sheets	12	$x$
Weight(in grams)	50	500

More number of sheets will weigh more.
So, it is a case of direct variation.
$$\begin{gathered} \mathrm{Now},\frac{12}{50}=\frac{x}{500} \\ \Rightarrow x=\frac{12\times 500}{50} \\ \Rightarrow x=120 \end{gathered}$$

∴ 120 sheets will weigh 500 g.