Advertisements
Advertisements
Question
In a library 136 copies of a certain book require a shelf-length of 3.4 metre. How many copies of the same book would occupy a shelf-length of 5.1 metres?
Advertisements
Solution
| Number of copies | 136 | x |
| Length the shelf (in m) | 3.4 | 5.1 |
Let x be the number of copies that would occupy a shelf-length of 5.1 m.
\[\text{ Since the number of copies and the length of the shelf are in direct variation, we have: } \]
\[\frac{136}{x} = \frac{3 . 4}{5 . 1}\]
\[ \Rightarrow 136 \times 5 . 1 = x \times 3 . 4\]
\[ \Rightarrow x = \frac{136 \times 5 . 1}{3 . 4}\]
\[ = 204\]
\[\text{ Thus, 204 copies will occupy a shelf of length 5 . 1 m } .\]
APPEARS IN
RELATED QUESTIONS
Following are the car parking charges near a railway station upto
| 4 hours | ₹60 |
| 8 hours | ₹100 |
| 12 hours | ₹140 |
| 24 hours | ₹180 |
Check if the parking charges are in direct proportion to the parking time.
A mixture of paint is prepared by mixing 1 part of red pigments with 8 parts of base. In the following table, find the parts of the base that need to be added.
| Parts of red pigment | 1 | 4 | 7 | 12 | 20 |
| parts of base | 8 | .... | .... | .... | .... |
In which of the following tables x and y vary directly?
(i)
| a | 7 | 9 | 13 | 21 | 25 |
| b | 21 | 27 | 39 | 63 | 75 |
(ii)
| a | 10 | 20 | 30 | 40 | 46 |
| b | 5 | 10 | 15 | 20 | 23 |
(iii)
| a | 2 | 3 | 4 | 5 | 6 |
| b | 6 | 9 | 12 | 17 | 20 |
(iv)
| a | 12 | 22 | 32 | 42 | 52 |
| b | 13 | 23 | 33 | 43 | 53 |
Complite the following table given that x varies directly as y .
| x | 2.5 | ... | ... | 15 |
| y | 5 | 8 | 12 | ... |
A and B can finish a work in 20 days. A alone can do \[\frac{1}{5}\] th of the work in 12 days. In how many days can B alone do it?
A cistern has two inlets A and B which can fill it in 12 hours and 15 hours respectively. An outlet can empty the full cistern in 10 hours. If all the three pipes are opened together in the empty cistern, how much time will they take to fill the cistern completely?
Both x and y are in direct proportion, then `1/x` and `1/y` are ______.
When the distance is kept fixed, speed and time vary directly with each other.
From the following table, determine if x and y are in direct proportion or not.
| x | 3 | 6 | 15 | 20 | 30 |
| y | 12 | 24 | 45 | 60 | 120 |
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?
