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प्रश्न
Fill in the blank in of the following so as to make the statement true:
x and y are said to vary directly with each other if for some positive number k ....,...... = k.
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उत्तर
\[\text{ x and y are said to vary directly with each other if } \frac{x}{y} = k,\text{ where k is a positive number } \] .
संबंधित प्रश्न
Explain the concept of direct variation.
Which of the following quantities vary directly with each other?
(i) Number of articles (x) and their price (y).
(ii) Weight of articles (x) and their cost (y).
(iii) Distance x and time y, speed remaining the same.
(iv) Wages (y) and number of hours (x) of work.
(v) Speed (x) and time (y) (distance covered remaining the same).
(vi) Area of a land (x) and its cost (y).
Mohan takes 9 hours to mow a large lawn. He and Sohan together can mow it in 4 hours. How long will Sohan take to mow the lawn if he works alone?
x and y are said to vary directly with each other if for some positive number k, ______ = k.
If x and y are in direct proportion, then (x – 1) and (y – 1) are also in direct proportion.
The area of cultivated land and the crop harvested is a case of direct proportion.
Write whether the following statement vary directly, vary inversely with each other, or neither of the two.
Area of land and its cost.
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?
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.
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?
