Exercise 10.3

1. Siri has enough money to buy 5 kg of potatoes at the price of ₹8 per kg. How much can she buy for the same amount if the price is increased to ₹10 per kg?

Solution:

Total money Siri has = kg × ₹ /kg = ₹

Quantity of potatoes she can buy at ₹10/kg = ₹40 /₹10/kg = kg

2. A camp has food stock for 500 people for 70 days. If 200 more people join the camp, how long will the stock last?

Solution:

Total food stock = people × days = person-days

Total people after joining = 500 + = people

Number of days the stock will last = 35000 person-days/700 people = days

3. 36 men can do a piece of work in 12 days. In how many days 9 men can do the same work?

Solution:

Total work = men × days = man-days

Number of days 9 men can do the work = 432 man-days/9 men = days

4. A tank can be filled by 5 pipes in 80 minutes. How long will it take to fill the tank by 8 pipes of the same size?

Solution:

Total filling capacity = pipes × minutes = pipe-minutes

Time taken by 8 pipes = 400 pipe-minutes/8 pipes = minutes

5. A ship can cover a certain distance in 10 hours at a speed of 16 nautical miles per hour. By how much should its speed be increased so that it takes only 8 hours to cover the same distance?

Solution:

Distance = Speed × Time = nautical miles/hour × hours = nautical miles

Required speed to cover the distance in 8 hours = 160 nautical miles/8 hours = nautical miles/hour

Increase in speed = - = nautical miles/hour

6. 5 pumps are required to fill a tank in 1 1/2 hours. How many pumps of the same type are used to fill the tank in half an hour?

Solution:

Time in hours = hours

Total pump-hours required = pumps × 1.5 hours = pump-hours

Number of pumps needed to fill in 0.5 hours = 7.5 pump-hours/0.5 hours = pumps

7. If 15 workers can build a wall in 48 hours, how many workers will be required to do the same work in 30 hours?

Solution:

Total work = workers × hours = worker-hours

Number of workers required to do the same work in 30 hours = 720 worker-hours/ 30 hours = workers

8. A School has 8 periods a day each of 45 minutes duration. How long would each period become, if the school has 6 periods a day? (assuming the number of school hours to be the same).

Solution:

Total school minutes = periods × minutes/period = minutes

Duration of each period with 6 periods a day = 360 minutes/6 periods = minutes

9. If z varies directly as x and inversely as y. Find the percentage increase in z due to an increase of 12 % in x and a decrease of 20 % in y.

Solution:

Given: z ∝ x and z ∝ 1/y, therefore z = k (where k is a constant)

Let x' = x + x = x (12% increase)

Let y' = y + y = y (20% decrease)

New value of z, z1 = kx1y1 = k(x)/(y) = kx/y = z

Percentage increase in z = [(z1 - z)/z] × 100 = ((z - z)/z) × 100 = × 100 = %

10. If x + 1 men will do the work in x + 1 days, find the number of days that (x + 2) men can finish the same work.

Solution:

Total work = (x + 1) men × (x + 1) days = x+12x+1 man-days

Number of days (x + 2) men can finish the same work = x+12x+1 man-days / men = x+12x+2x+12x+1 days.

11. Given a rectangle with a fixed perimeter of 24 meters, if we increase the length by 1m the width and area will vary accordingly. Use the following table of values to look at how the width and area vary as the length varies. What do you observe? Write your observations in your notebooks.

Solution:

Since the perimeter is 24 meters (or 2400 cm), 2(Length + Width) = 2400, so Length + Width = .

Therefore, Width = 1200 - Length with Area = Length × Width.