Ratio - Study Mode
[#181] In a school, $$frac{5}{{12}}$$ of the number of students are girls and the rest are boys. $$frac{4}{7}$$ of the number of boys are below 14 years of age, and $$frac{2}{5}$$ of the number of girls are 14 years or above 14 years of age. If the number of students below 14 years of age is 1120, then the total number of students in the school is:
Correct Answer
(D) 1920
Explanation
Solution: Let total student = 12 unit B : G 7 : 5 B → $$frac{4}{7}$$ xa0 (14 year less) B = 4 xa0 (14 year less) G → $$frac{2}{5}$$ G = 3 xa0 (14 year less) Total student less than 14 year = 4 + 3 = 7 7 → 1120 1 → 160 12 → 1920 total student
[#182] How much will be decreased to each terms of ratio 16 : 19, so that it will be 7 : 6?
Correct Answer
(A) 37
Explanation
Solution: Let, each term be 16a and 19a, and the number subtracted from it is x. $$frac{{16a - x}}{{19a - x}} = frac{7}{6}$$ ⇒ 96a - 6x = 133a - 7x ⇒ x = 133a - 96a ⇒ x = 37a Hence, the number will be the multiple of 37. So, from option A is a right answer.
[#183] What is the third proportional to 16 and 24?
Correct Answer
(A) 36
Explanation
Solution: Third proportional of 16 and 24 $$ = frac{{{b^2}}}{a} = frac{{24 imes 24}}{{16}} = 36$$
[#184] The salaries of Vipin and Dinesh are in the ratio 5 : 8. If the salary of each is increased by 4,800, then new ratio becomes 7 : 10. What is Vipin's salary?
Correct Answer
(A) Rs. 12,000
Explanation
Solution: Let the salary of Vipin and Dinesh be 5$$x$$ and 8$$x$$ $$eqalign{
& frac{{5x + 4800}}{{8x + 4800}} = frac{7}{{10}} cr
& Rightarrow 50x + 48000 = 56x + 33600 cr
& Rightarrow x = frac{{14400}}{6} cr
& Rightarrow x = 2400 cr} $$ ∴ Vipin's salary is Rs. 12000
[#185] The ratio of the length and the perimeter of a rectangle is 2 : 7. What is the ratio of the length and breadth of the rectangle?
Correct Answer
(A) 4 : 3
Explanation
Solution: $$eqalign{
& frac{l}{{2left( {l + b}
ight)}} = frac{2}{7} cr
& Rightarrow 7l = 4l + 4b cr
& Rightarrow 3l = 4b cr
& Rightarrow frac{l}{b} = frac{4}{3} = 4:3 cr} $$