Page 236 - Start Up Mathematics_6

8. An aeroplane covers a distance of 2,550 km in 3 hours. How much distance will it cover in
7 hours? Assume that flying conditions remain the same.

9. A transport company charges ` 1,800 to carry 24 boxes. How much will it charge for 18
such boxes?
10. A truck requires 108 L of diesel for covering a distance of 594 km. How much diesel will
the truck require to cover a distance of 1,650 km?
11. A machine produces 240 m of cloth in 4 hours. How many metres of cloth will be produced
in 6 days, if the factory runs for 18 hours a day?

At a Glance

a
1. The ratio of two quantities a and b expressed in the same units is the fraction . It shows
b
how many times one quantity is of the other. Ratio of two numbers a and b is also denoted
by a : b where a is the first term and b is the second term.
2. A ratio is said to be in the simplest form if the two terms of the ratio have no common factors
other than 1.

3. Equivalent ratios have the same simplest form. By multiplying or dividing the numerator
and denominator by the same non-zero number we get equivalent ratios.
4. If two ratios are equal, we say that they are in proportion, i.e., four quantities a, b, c and d
a c
are in proportion, iff b = d . The numbers a and d are called extremes and b and c are called
means.
5. If b = ac then the numbers a, b and c are said to be in continued proportion. The number
2
b is called the mean proportion of a and c.
6. The method of finding the value of one unit and then the value of required number of units
is known as unitary method.

Review Exercises

Multiple ChoiCe Questions
1. For the ratio to be meaningful the terms should have:

(a) same units (b) same value (c) same factors (d) different units
2. If 1, 2, 3 and x are in proportion, then the value of x is:

(a) 3 (b) 4 (c) 5 (d) 6
3. Gaurav earns ` 1,200 in 10 days. In 18 days he will earn:

(a) ` 2,160 (b) ` 2,000 (c) ` 1,960 (d) ` 2,250
4. If q is the mean proportion of p and r then the value of q is:
pr
(a) pr (b) (pr) 2 (c) pr (d) 2
5. If p : q :: r : s, then the proportion not implied is:

(a) q : p :: s : r (b) p : r :: q : s (c) q : p :: r : s (d) s : q :: r : p

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