Proportional Reasoning - 2 | FIO

Question 22

A car takes 2 hours to reach a destination, travelling at a speed of 60 km/h. How long will the car take if it travels at a speed of 80 km/h?

Solution

For a fixed distance, speed and time are inversely proportional. This means that if one increases, the other decreases, and their product remains constant.

Step 1 — Set up the relationship

Let $S_1$ be the initial speed of the car. Let $T_1$ be the initial time taken. Let $S_2$ be the new speed of the car. Let $T_2$ be the new time taken. Since speed and time are inversely proportional for a fixed distance, their product is constant.

$S_1 \times T_1 = S_2 \times T_2$

We are given the initial speed $S_1 = 60 \text{ km/h}$ . The initial time taken is $T_1 = 2 \text{ hours}$ . The new speed is $S_2 = 80 \text{ km/h}$ . We need to find the new time, $T_2$ .

Diagram 1

Step 2 — Calculate the new time

Let us substitute the known values into our equation.

$60 \text{ km/h} \times 2 \text{ hours} = 80 \text{ km/h} \times T_2$

First, we multiply the numbers on the left side.

$120 = 80 \times T_2$

Now, we need to find the value of $T_2$ . We divide both sides of the equation by 80.

$T_2 = \frac{120}{80}$

We can simplify this fraction by dividing the numerator and denominator by 10.

$T_2 = \frac{12}{8}$

Then, we divide both by 4.

$T_2 = \frac{3}{2}$

Finally, we convert the fraction to a decimal.

$T_2 = 1.5 \text{ hours}$

$\boxed{1.5 \text{ hours}}$

Answer

(i) The car will take 1.5 hours.

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Q10

Fill in the empty cells if x and y are in inverse proportion.

Q11

Which of the following pairs of quantities are in inverse proportion?

(i) The number of taps filling a water tank and the time taken to fill it.

(ii) The number of painters hired and the days needed to paint a wall of fixed size.

(iii) The distance a car can travel and the amount of petrol in the tank.

(iv) The speed of a cyclist and the time taken to cover a fixed route.

(v) The length of cloth bought and the price paid at a fixed rate per metre.

(vi) The number of pages in a book and the time required to read it at a fixed reading speed.

Q12

If 24 pencils cost ₹120, how much will 20 such pencils cost?

Q13

A tank on a building has enough water to supply 20 families living there for 6 days. If 10 more families move in there, how long will the water last? What assumptions do you need to make to work out this problem?

Q14

Fill in the average number of hours each living being sleeps in a day by looking at the charts. Select the appropriate hours from this list: 15, 2.5, 20, 8, 3.5, 13, 10.5, 18.

Q15

The pie chart on the right shows the result of a survey carried out to find the modes of transport used by children to go to school. Study the pie chart and answer the following questions.

(i) What is the most common mode of transport?

(ii) What fraction of children travel by car?

(iii) If 18 children travel by car, how many children took part in the survey? How many children use taxis to travel to school?

(iv) By which two modes of transport are equal numbers of children travelling?

Q16

Three workers can paint a fence in 4 days. If one more worker joins the team, how many days will it take them to finish the work? What are the assumptions you need to make?

Q17

It takes 6 hours to fill 2 tanks of the same size with a pump. How long will it take to fill 5 such tanks with the same pump?

Q18

A given set of chairs are arranged in 25 rows, with 12 chairs in each row. If the chairs are rearranged with 20 chairs in each row, how many rows does this new arrangement have?

Q19

A school has 8 periods a day, each of 45 minutes duration. How long is each period, if the school has 9 periods a day, assuming that the number of school hours per day stays the same?

Q20

A small pump can fill a tank in 3 hours, while a large pump can fill the same tank in 2 hours. If both pumps are used together, how long will the tank take to fill?

Q21

A factory requires 42 machines to produce a given number of toys in 63 days. How many machines are required to produce the same number of toys in 54 days?

Q22

A car takes 2 hours to reach a destination, travelling at a speed of 60 km/h. How long will the car take if it travels at a speed of 80 km/h?