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2. Given that x and y are in direct variation from each other in the following table. Find the constant
of variation and the missing values of x and y.

x 9 12 x 1 36 x 2 51
y 12 16 28 y 1 84 y 2
3. It is given that l varies directly as m.

(a) Write an equation which relates l and m.
(b) Find the constant of proportion (k), when l is 6 and m is 18.

(c) Find l, when m is 33.
(d) Find m, when l is 8.
4. The variable x varies directly as y and x = 80 when y is 160. What is y when x is 64?

5. A car covers 270 km in 27 L petrol. How much distance would it cover in 15.5 L petrol?
6. A train is moving at a uniform speed of 72 km/h.

(a) How far will it travel in 15 minutes?
(b) Find the time requires to cover a distance of 400 km.

7. Kanika typed 1,440 words in 1 hour 20 minutes. How many words would she type in 42 minutes?
2
2
8. For a yoga programme, 75 persons need 250 m of space. If the available space is 60 m , how many
persons can perform yoga?
7
9. If 3 kg of sugar contains 1.35 × 10 crystals, then find the number of crystals in 7 kg of sugar.
10. If a deposit of `5,000 earns an interest of `1,250 in 3 years, how much interest would a deposit of
`48,000 earn in 3 years with the same rate of simple interest?
11. The scale of a map is 1 : 3,50,00,000. The two cities are 4.8 cm apart on the map. Find the actual
distance between the two in km.

12. The mass of an aluminium rod varies directly with its length. If a 16 cm long rod has a mass of
192 g, find (a) the length of the rod whose mass is 108 g, and (b) the mass of the rod whose length
is 24.5 cm.

13. A tree of height 9.5 m casts a shadow of 8 m long. At the same time, if a water tank casts a shadow
of 21 m long, then find the height of the tank.

X
9.5 m

8 m 21 m

14. Rajat’s father gifted him a Casio on his birthday. Rajat finds a pattern in its keyboard as shown.
(a) Find the ratio of white keys to black keys on the keyboard.

(b) How many white keys would you expect on a keyboard if there are
160 black keys on it?

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