Question : The ratio of the ages of two boys is 5 : 6. After two years, the ratio will be 7 : 8. Determine the ratio of their ages after 12 years.
Option 1: $\frac{22}{24}$
Option 2: $\frac{15}{16}$
Option 3: $\frac{17}{18}$
Option 4: $\frac{11}{12}$
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Correct Answer: $\frac{17}{18}$
Solution : Given: The ratio of the age of two boys is 5 : 6. After two years, the ratio will be 7 : 8. Let the age of two boys be $5x$ years and $6x$ years respectively. As per conditions, we have: $\frac{5x+2}{6x+2}=\frac{7}{8}$ ⇒ $40x+16=42x+14$ ⇒ $2x=2$ ⇒ $x=1$ Required ratio after 12 years, = $(5x+12):(6x+12)$ = (5 + 12) : (6 + 12) = 17 : 18 Hence, the correct answer is $\frac{17}{18}$.
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Question : The sum of the present ages of a father and his son is 94 years. 8 years ago their respective ages were in the ratio of 2 : 1. After 10 years what will be the ratio of ages of father and son?
Option 1: 35 : 22
Option 2: 14 : 13
Option 3: 25 : 18
Option 4: 16 : 15
Question : The ratio of the present age of two girls is 3 : 4. After two years, the ratio will be 7 : 9. Which of the following statement(s) is/are correct? I. The ratio of their ages after 10 years is 6 : 7. II. The ratio of their ages after 12 years is 6 : 7.
Option 1: Both I and II
Option 2: Only II
Option 3: Neither I nor II
Option 4: Only I
Question : The ratio of the father's age to his son's age is 5 : 3. The product of the numbers representing their ages is 960. The ratio of their ages after 6 years will be:
Option 1: 23 : 15
Option 2: 23 : 17
Option 3: 21 : 15
Option 4: 21 : 17
Question : The current ages of Sonali and Monali are in the ratio 5 : 3. Five years from now, their ages will be in the ratio of 10 : 7. Determine Monali's current age.
Option 1: 5 years
Option 2: 3 years
Option 3: 9 years
Option 4: 15 years
Question : If $\sec A=\frac{17}{15}$, then what is the value of $\cot A$?
Option 1: $\frac{15}{21}$
Option 2: $\frac{15}{7}$
Option 3: $\frac{8}{15}$
Option 4: $\frac{15}{8}$
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