Ratio - Study Mode

[#86] Two numbers are in the ratio of 3 : 5. If 9 is subtracted from each, they are in the ratio of 12 : 23. What is the large number?
Correct Answer

(C) 55

Explanation

Solution: Let the numbers be 3x and 5x Then, $$ = frac{{3x - 9}}{{5x - 9}} = frac{{12}}{{23}}$$ ⇒ 23(3x - 9) = 12(5x - 9) ⇒ 69x - 207 = 60x - 108 ⇒ 9x = 99 ⇒ x = 11 ∴ Largest number = 5 × 11 = 55

[#87] A mixture contains milk and water in the ratio 5 : 1. On adding 5 litres of water, the ratio of milk and water becomes 5 : 2. The quantity of milk in the mixture is = ?
Correct Answer

(B) 25 litres

Explanation

Solution: Initial Ratio of Milk and water = 5 : 1 = 5x : 1x After adding 5 litres of water in the mixture, Ratio of Milk and water 5 : 2 = 5x : 2x Water 1 unit ratio increase by adding 5 litres of water. i.e x = 5 The quantity of milk in the mixture = 5 × 5 = 25 litres

[#88] The sides of a triangle are in the ratio of 7 : 9 : 12. The difference between the length of largest and smaller sides is 15 c.m. The length of the largest sides would be = ?
Correct Answer

(A) 36 cm

Explanation

Solution: Sides of a triangle are in the ratio of 7 : 9 : 12 i.e. 7x : 9x : 12x Difference between the length of largest and smaller sides = 12x - 7x = 15 ⇒ x = 3 ∴ largest sides would be 12 × 3 = 36cm

[#89] The three successive angles of a cycle quadrilateral are in the ratio 1 : 3 : 4, find the measure of the fourth angle ?
Correct Answer

(A) 72°

Explanation

Solution: Sum of the opposite angles in cyclic quadrilateral is 180° ∠A + ∠C = 180° ⇒ x + 4x = 180° ∴ x = 36° Now ∠B = 3x = 3 × 36° = 108° ∠D = 180 - ∠B = 180 - 108 = 72°

[#90] In a certain company, the ratio of the number of managers to the number of production - line workers is 5 to 72. If 8 additional production - line workers were to be hired, the ratio of the number of managers to the production - line workers would be 5 to 74. How many managers does the company have ?
Correct Answer

(B) 20

Explanation

Solution: Let the number of managers and production - line workers be 5x and 72x respectively Then, $$eqalign{
& = frac{{5x}}{{72x + 8}} = frac{5}{{74}} cr
& Rightarrow 370x = 360x + 40 cr
& Rightarrow 10x = 40 cr
& Rightarrow x = 4. cr} $$ ∴ Number of managers = 5 × 4 = 20