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30 persons can reap a field in 17 days. How many more persons should be engaged to reap the same field in 10 days?
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Shabnam takes 20 minutes to reach her school if she goes at a speed of 6 km/h. If she wants to reach school in 24 minutes, what should be her speed?
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Ravi starts for his school at 8:20 a.m. on his bicycle. If he travels at a speed of 10 km/h, then he reaches his school late by 8 minutes but on travelling at 16 km/h he reaches the school 10 minutes early. At what time does the school start?
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Match each of the entries in Column I with the appropriate entry in Column II
| Column I | Column II |
| 1. x and y vary inversely to each other | A. `x/y` = Constant |
| 2. Mathematical representation of inverse variation of quantities p and q |
B. y will increase in proportion |
| 3. Mathematical representation of direct variation of quantities m and n |
C. xy = Constant |
| 4. When x = 5, y = 2.5 and when y = 5, x = 10 | D. `p oo 1/q` |
| 5. When x = 10, y = 5 and when x = 20, y = 2.5 | E. y will decrease in proportion |
| 6. x and y vary directly with each other | F. x and y are directly proportional |
| 7. If x and y vary inversely then on decreasing x | G. `m oo n` |
| 8. If x and y vary directly then on decreasing x | H. x and y vary inversely |
| I. `p oo q` | |
| J. `m oo 1/n` |
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There are 20 grams of protein in 75 grams of sauted fish. How many grams of protein is in 225 gm of that fish?
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Ms. Anita has to drive from Jhareda to Ganwari. She measures a distance of 3.5 cm between these villages on the map. What is the actual distance between the villages if the map scale is 1 cm = 10 km?
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A water tank casts a shadow 21 m long. A tree of height 9.5 m casts a shadow 8 m long at the same time. The lengths of the shadows are directly proportional to their heights. Find the height of the tank.
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The table shows the time four elevators take to travel various distances. Find which elevator is fastest and which is slowest.
| Distance (m) | Time (sec.) | |
| Elevator- A | 435 | 29 |
| Elevator- B | 448 | 28 |
| Elevator- C | 130 | 10 |
| Elevator- D | 85 | 5 |
How much distance will be travelled by elevators B and C separately in 140 sec? Who travelled more and by how much?
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A volleyball court is in a rectangular shape and its dimensions are directly proportional to the dimensions of the swimming pool given below. Find the width of the pool.
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A recipe for a particular type of muffins requires 1 cup of milk and 1.5 cups of chocolates. Riya has 7.5 cups of chocolates. If she is using the recipe as a guide, how many cups of milk will she need to prepare muffins?
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Pattern B consists of four tiles like pattern A. Write a proportion involving red dots and blue dots in pattern A and B. Are they in direct proportion? If yes, write the constant of proportion.
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A bowler throws a cricket ball at a speed of 120 km/h. How long does this ball take to travel a distance of 20 metres to reach the batsman?
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Here is a key board of a harmonium:
- Find the ratio of white keys to black keys on the keyboard.
- What is the ratio of black keys to all keys on the given keyboard.
- This pattern of keys is repeated on larger keyboard. How many black keys would you expect to find on a keyboard with 14 such patterns.
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Here is a keyboard of a harmonium: What is the ratio of black keys to all keys on the given keyboard.
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Here is a keyboard of a harmonium: This pattern of keys is repeated on larger keyboard. How many black keys would you expect to find on a keyboard with 14 such patterns.
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The following table shows the distance travelled by one of the new eco-friendly energy-efficient cars travelled on gas.
| Litres of gas | 1 | 0.5 | 2 | 2.5 | 3 | 5 |
| Distance (km) | 15 | 7.5 | 30 | 37.5 | 45 | 75 |
Which type of properties are indicated by the table? How much distance will be covered by the car in 8 litres of gas?
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Kritika is following this recipe for bread. She realises her sister used most of sugar syrup for her breakfast. Kritika has only `1/6` cup of syrup, so she decides to make a small size of bread. How much of each ingredient shall she use?
Bread recipe
1 cup quick cooking oats
2 cups bread flour
`1/3` cup sugar syrup
1 tablespoon cooking oil
`1 1/3` cups water
3 tablespoons yeast
1 teaspoon salt.
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Many schools have a recommended students-teacher ratio as 35:1. Next year, school expects an increase in enrolment by 280 students. How many new teachers will they have to appoint to maintain the students-teacher ratio?
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Kusum always forgets how to convert miles to kilometres and back again. However she remembers that her car’s speedometer shows both miles and kilometres. She knows that travelling 50 miles per hour is same as travelling 80 kilometres per hour. To cover a distance of 200 km, how many miles Kusum would have to go?
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The students of Anju’s class sold posters to raise money. Anju wanted to create a ratio for finding the amount of money her class would make for different numbers of posters sold. She knew they could raise Rs 250 for every 60 posters sold.
- How much money would Anju’s class make for selling 102 posters?
- Could Anju’s class raise exactly Rs 2,000? If so, how many posters would they need to sell? If not, why?
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