Ratio & Proportion — Analytical & Application Based Questions

The mean proportion between two numbers is 6 and their third proportion is 48. Find the two numbers.

Answer

Let the numbers be a and b.

Given,

Mean proportion between the numbers is 6.

$\therefore \dfrac{a}{6} = \dfrac{6}{b}$

⇒ ab = 36

⇒ a = $\dfrac{36}{b}$ .....(1)

Third proportion of the numbers is 48.

$\therefore \dfrac{a}{b} = \dfrac{b}{45}$

⇒ b² = 48a

⇒ b² = 48 × $\dfrac{36}{b}$

⇒ b³ = 1728

⇒ b = $\sqrt[3]{1728}$

⇒ b = 12.

Substituting value of b in equation (1), we get :

⇒ a = $\dfrac{36}{12}$ = 3

Hence, the numbers are 3 and 12.

The profit in rupees in a local restaurant and the number of customers who visited the restaurant are tabulated below for each week for one month.

Find :

(a) if the number of customers and profit per week in continued proportion or not? Justify your answer.

(b) the value of x and y.

Answer

(a) Since,

$\dfrac{1400}{28000} = \dfrac{5600}{112000} = \dfrac{1}{20}$

Thus, number of customers and profit per week are in direct proportion not in continued proportion.

Hence, number of customers and profit per week are not in continued proportion.

(b) As,

Number of customers and profit per week are in proportion.

$\therefore \dfrac{x}{32140} = \dfrac{1}{20}$

$\Rightarrow x = 32140 \times \dfrac{1}{20} = 1607$

and

$\therefore \dfrac{3212}{y} = \dfrac{1}{20}$

⇒ y = 3212 × 20 = 64240.

Hence, x = 1607 and y = 64240.