Q1. Age of Mona is twelve times that of her daughter Ankita. If Ankita's age is 3 yrs, then How old is Mona?
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$\therefore$ Mona's age = $3 \times 12 = 36$ yrs Ans
Q2. The present ages of Rakesh and Saurabh are 20 yrs and 24 yrs. Find the ratio between Rakesh's age 4 yrs ago and Saurabh's age 4 yrs hence.
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$\Rightarrow \dfrac{\text{Rakesh's age} - 4}{\text{Saurabh's age} + 4} = \dfrac{20 - 4}{24 + 4}$
$\Rightarrow \dfrac{16}{28} = \dfrac{4}{7} = 4:7$ Ans
$\Rightarrow \dfrac{16}{28} = \dfrac{4}{7} = 4:7$ Ans
Q3. The age of Mother 4 yrs ago was 8 times the age of her son. At present, the Mother's age is 4 times that of her son. Find son's current age and present ratio between their age.
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$\Rightarrow$ Let son's age be = $x$ yrs
$\therefore$ Mother's age = $4x$
$\Rightarrow$ Mother's age 4 yrs ago = $(4x - 4)$
$\Rightarrow$ Son's age 4 yrs ago = $(x - 4)$
$\Rightarrow$ Given, Mother's age 4 yrs ago was 8 times that of her son:
$\therefore (4x - 4) = 8(x - 4)$
$\Rightarrow 4x - 4 = 8x - 32$
$\Rightarrow 32 - 4 = 8x - 4x$
$\Rightarrow 28 = 4x$
$\Rightarrow x = \dfrac{28}{4} = 7$
$\Rightarrow$ Current age of Son = 7 yrs Ans
$\Rightarrow$ Given, Mother's Cuurent age is 4 times that of her son:
$\therefore$ Mother's present age = $7 \times 4 = 28$ yrs
$\Rightarrow$ Required ratio = $\dfrac{28}{7} = \dfrac{4}{1} = 4:1$ Ans
$\therefore$ Mother's age = $4x$
$\Rightarrow$ Mother's age 4 yrs ago = $(4x - 4)$
$\Rightarrow$ Son's age 4 yrs ago = $(x - 4)$
$\Rightarrow$ Given, Mother's age 4 yrs ago was 8 times that of her son:
$\therefore (4x - 4) = 8(x - 4)$
$\Rightarrow 4x - 4 = 8x - 32$
$\Rightarrow 32 - 4 = 8x - 4x$
$\Rightarrow 28 = 4x$
$\Rightarrow x = \dfrac{28}{4} = 7$
$\Rightarrow$ Current age of Son = 7 yrs Ans
$\Rightarrow$ Given, Mother's Cuurent age is 4 times that of her son:
$\therefore$ Mother's present age = $7 \times 4 = 28$ yrs
$\Rightarrow$ Required ratio = $\dfrac{28}{7} = \dfrac{4}{1} = 4:1$ Ans
Q4. Present ratio between ages of Prem and Akash is 4:3. After 6 yrs, Prem's age will be 26 yrs. Find Akash's present age and ratio between their age 6 yrs hence?
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$\Rightarrow$ Let age of Prem and Akash be = $4x \text{ and } 3x$ yrs
$\Rightarrow$ Given, after 6 yrs Prem's age will be = 26 yrs
$\therefore 4x + 6 = 26 \Rightarrow 4x = 26 - 6 \Rightarrow 4x = 20$
$\Rightarrow x = \dfrac{20}{4} = 5$
$\therefore$ Prem's present age = $4 \times 5 = 20$ yrs
$\Rightarrow$ Akash's present Age = $3 \times 5 = 15$ yrs Ans
$\therefore$ Required ratio = $\dfrac{20 + 6}{15 + 6} = \dfrac{26}{21} = 26:21$ Ans
$\Rightarrow$ Given, after 6 yrs Prem's age will be = 26 yrs
$\therefore 4x + 6 = 26 \Rightarrow 4x = 26 - 6 \Rightarrow 4x = 20$
$\Rightarrow x = \dfrac{20}{4} = 5$
$\therefore$ Prem's present age = $4 \times 5 = 20$ yrs
$\Rightarrow$ Akash's present Age = $3 \times 5 = 15$ yrs Ans
$\therefore$ Required ratio = $\dfrac{20 + 6}{15 + 6} = \dfrac{26}{21} = 26:21$ Ans
Q5. Present ages of Jasmine and Karuna are in the ratio 5:4. 3 yrs hence, the ratio of their ages will become 11:9. Find their present ages.
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$\Rightarrow$ Let present ages of Jasmine and Karuna be = $5x \text{ and } 4x$ yrs
$\Rightarrow$ As such, we have:
$\Rightarrow \dfrac{5x + 3}{4x + 3} = \dfrac{11}{9}$
$\Rightarrow 9(5x + 3) = 11(4x + 3)$
$\Rightarrow 45x + 27 = 44x + 33$
$\Rightarrow 45x - 44x = 33 - 27$
$\Rightarrow x = 6$
$\therefore$ Jasmine's present age = $5 \times 6 = 30$ yrs Ans
$\Rightarrow$ Karuna's present age = $4 \times 6 = 24$ yrs Ans
$\Rightarrow$ As such, we have:
$\Rightarrow \dfrac{5x + 3}{4x + 3} = \dfrac{11}{9}$
$\Rightarrow 9(5x + 3) = 11(4x + 3)$
$\Rightarrow 45x + 27 = 44x + 33$
$\Rightarrow 45x - 44x = 33 - 27$
$\Rightarrow x = 6$
$\therefore$ Jasmine's present age = $5 \times 6 = 30$ yrs Ans
$\Rightarrow$ Karuna's present age = $4 \times 6 = 24$ yrs Ans
Q6. The age of a boy is twice of his sister's age. If sum of their ages is 30, find their present age and ratio.
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$\Rightarrow$ Let sisters age be = $x$
$\therefore$ Boy's age = $2x$
As per given, we have:
$\Rightarrow 2x + x = 30$
$\Rightarrow 3x = 30$
$\Rightarrow x = \dfrac{30}{3} = 10$
$\therefore$ Boy's age = $10 \times 2 = 20$ yrs
$\Rightarrow$ And, sister's age = $10 \times 1 = 10$ yrs
$\Rightarrow$ Required ratio = $\dfrac{20}{10} = \dfrac{2}{1} = 2:1$ Ans
$\therefore$ Boy's age = $2x$
As per given, we have:
$\Rightarrow 2x + x = 30$
$\Rightarrow 3x = 30$
$\Rightarrow x = \dfrac{30}{3} = 10$
$\therefore$ Boy's age = $10 \times 2 = 20$ yrs
$\Rightarrow$ And, sister's age = $10 \times 1 = 10$ yrs
$\Rightarrow$ Required ratio = $\dfrac{20}{10} = \dfrac{2}{1} = 2:1$ Ans
Q7. Anisha is 8 yrs younger than hir sister Ankita. How old will Ankita be when she is twice as old as Anisha?
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$\Rightarrow$ Let Anisha's age be = $x$
$\therefore$ Ankita's age = $(x + 8)$
$\Rightarrow$ Twice of Anisha's age will be = $2x$
So, we have the equation:
$\Rightarrow x + 8 = 2x$
$\Rightarrow 8 = 2x - x$
$\Rightarrow x = 8$
$\therefore$ Ankita's age = $8 + 8 = 16$ yrs Ans
$\therefore$ Ankita's age = $(x + 8)$
$\Rightarrow$ Twice of Anisha's age will be = $2x$
So, we have the equation:
$\Rightarrow x + 8 = 2x$
$\Rightarrow 8 = 2x - x$
$\Rightarrow x = 8$
$\therefore$ Ankita's age = $8 + 8 = 16$ yrs Ans
Q8. Sachin's father's age is 4 times Sachin's age. Five years ago; father's age was 7 times of the age of his son's age; find father's present age and their ratio.
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$\Rightarrow$ Let Sachin's age be = $x$ yrs
$\therefore$ Father's age = $4x$ yrs
Given, five yrs ago father's age was 7 times than Sachin:
$\Rightarrow 7(x - 5) = 4x - 5$
$\Rightarrow 7x - 35 = 4x - 5$
$\Rightarrow 7x - 4x = 35 - 5$
$\Rightarrow 3x = 30$
$\Rightarrow x = \dfrac{30}{3} = 10$ (Sachin's age)
$\therefore$ Father's age = $4 \times 10 = 40$ yrs Ans
$\Rightarrow$ Required ratio = $\dfrac{40}{10} = \dfrac{4}{1} = 4:1$ Ans
$\therefore$ Father's age = $4x$ yrs
Given, five yrs ago father's age was 7 times than Sachin:
$\Rightarrow 7(x - 5) = 4x - 5$
$\Rightarrow 7x - 35 = 4x - 5$
$\Rightarrow 7x - 4x = 35 - 5$
$\Rightarrow 3x = 30$
$\Rightarrow x = \dfrac{30}{3} = 10$ (Sachin's age)
$\therefore$ Father's age = $4 \times 10 = 40$ yrs Ans
$\Rightarrow$ Required ratio = $\dfrac{40}{10} = \dfrac{4}{1} = 4:1$ Ans
Q9. John and his Uncle's age differ by 30 yrs. After 7 yrs; if the sum of their ages is 66; find their present ages and ratio between their age 7 years hence?
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$\Rightarrow$ Let John's age be = $x$ yrs
$\Rightarrow$ Let Uncle's age be = $y$ yrs
Given difference = $y - x = 30$....(i)
Post seven years:
$\Rightarrow$ Provided sum of age = $(y + 7) + (x + 7) = 66$....(ii)
From equation (i) we have:
$\Rightarrow y = 30 + x$
Now, putting y in equation (ii) we have:
$\Rightarrow (30 + x + 7) + (x + 7) = 66$
$\Rightarrow 2x + 44 = 66$
$\Rightarrow 2x = 66 - 44$
$\Rightarrow 2x = 22$
$\Rightarrow x = \dfrac{22}{2} = 11$
$\therefore$ John's age = $11$ yrs. Ans
$\Rightarrow$ His uncle's age = $y - 18 = 30$
$\Rightarrow y = 30 + 11 = 41$ yrs Ans
$\therefore$ Required ratio = $\dfrac{41}{11} = 41:11$ Ans
$\Rightarrow$ Let Uncle's age be = $y$ yrs
Given difference = $y - x = 30$....(i)
Post seven years:
$\Rightarrow$ Provided sum of age = $(y + 7) + (x + 7) = 66$....(ii)
From equation (i) we have:
$\Rightarrow y = 30 + x$
Now, putting y in equation (ii) we have:
$\Rightarrow (30 + x + 7) + (x + 7) = 66$
$\Rightarrow 2x + 44 = 66$
$\Rightarrow 2x = 66 - 44$
$\Rightarrow 2x = 22$
$\Rightarrow x = \dfrac{22}{2} = 11$
$\therefore$ John's age = $11$ yrs. Ans
$\Rightarrow$ His uncle's age = $y - 18 = 30$
$\Rightarrow y = 30 + 11 = 41$ yrs Ans
$\therefore$ Required ratio = $\dfrac{41}{11} = 41:11$ Ans
Q10. 5 years ago, the average age of A and B was 15 years. At present the average age of A, B and C is 20 years. Find C's age 10 years hence.
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$\Rightarrow$ Combined age of A and B = $15 \times 2 = 30$ yrs.
$\Rightarrow$ Increment in age of A and B 5 yrs hence = $5 + 5 = 10$
$\therefore$ New Combined age at present = $30 + 10 = 40$ yrs
$\Rightarrow$ Combined age of A, B and C = $20 \times 3 = 60$ yrs.
So, we have the equation:
$\Rightarrow 40 + \text{ R } = 60$
$\Rightarrow \text{ R } = 60 - 40$
$\Rightarrow \text{ R } = 20$
$\therefore$ R's age 10 yrs hence = $20 + 10 = 30$ yrs Ans
$\Rightarrow$ Increment in age of A and B 5 yrs hence = $5 + 5 = 10$
$\therefore$ New Combined age at present = $30 + 10 = 40$ yrs
$\Rightarrow$ Combined age of A, B and C = $20 \times 3 = 60$ yrs.
So, we have the equation:
$\Rightarrow 40 + \text{ R } = 60$
$\Rightarrow \text{ R } = 60 - 40$
$\Rightarrow \text{ R } = 20$
$\therefore$ R's age 10 yrs hence = $20 + 10 = 30$ yrs Ans
Q11. The present age of Anuj is $\dfrac{2}{5}$ of his mother. After 8 years; Anuj's age becomes $\dfrac{1}{2}$ of his mother. Find their present age and ratio between the two.
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$\Rightarrow$ Let mother's age be = $x$ yrs
$\therefore$ Anuj's age = $\dfrac{2}{5} \text{ of } x = \dfrac{2x}{5}$
Given, 8 yrs hence Anuj's age becomes half of his mother:
$\Rightarrow \dfrac{1}{2}(x + 8) = \dfrac{2}{5}x + 8$
$\Rightarrow \dfrac{x}{2} + \dfrac{8}{2} = \dfrac{2}{5}x + 8$
$\Rightarrow \dfrac{x}{2} -\dfrac{2x}{5} = 8 - \dfrac{8}{2}$
$\Rightarrow \dfrac{5x - 4x}{10} = \dfrac{16 - 8}{2}$
$\Rightarrow \dfrac{x}{10} = \dfrac{8}{2}$
$\Rightarrow \dfrac{x}{10} = 4$
$\Rightarrow x = 4 \times 10 = 40$ yrs
$\therefore$ Mother's age = 40 yrs Ans
$\Rightarrow$ Anuj's age = $\dfrac{2}{5} \text{ of } 40 = 2 \times 8 = 16$ yrs Ans
$\therefore$ Required ratio = $\dfrac{40}{16} = \dfrac{5}{2} = 8:2$ Ans
$\therefore$ Anuj's age = $\dfrac{2}{5} \text{ of } x = \dfrac{2x}{5}$
Given, 8 yrs hence Anuj's age becomes half of his mother:
$\Rightarrow \dfrac{1}{2}(x + 8) = \dfrac{2}{5}x + 8$
$\Rightarrow \dfrac{x}{2} + \dfrac{8}{2} = \dfrac{2}{5}x + 8$
$\Rightarrow \dfrac{x}{2} -\dfrac{2x}{5} = 8 - \dfrac{8}{2}$
$\Rightarrow \dfrac{5x - 4x}{10} = \dfrac{16 - 8}{2}$
$\Rightarrow \dfrac{x}{10} = \dfrac{8}{2}$
$\Rightarrow \dfrac{x}{10} = 4$
$\Rightarrow x = 4 \times 10 = 40$ yrs
$\therefore$ Mother's age = 40 yrs Ans
$\Rightarrow$ Anuj's age = $\dfrac{2}{5} \text{ of } 40 = 2 \times 8 = 16$ yrs Ans
$\therefore$ Required ratio = $\dfrac{40}{16} = \dfrac{5}{2} = 8:2$ Ans
Q12. Savita is 4 yrs older than Binita. 16 years hence, Savita will be thrice of her present age and Binita will be five times of her present age. Find their present ages. Also, find the ratio between their age after 16 years.
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$\Rightarrow$ Let Binita's age be = $x$ yrs
$\therefore$ Savita's age = $x + 4$
$\Rightarrow$ Savita's age after 16 yrs = $3(x + 4) = 3x + 12$
So, we have the equation:
$\Rightarrow (x + 4) + 16 = 3x + 12$
$\Rightarrow x + 20 = 3x + 12$
$\Rightarrow 20 - 12 = 3x - x$
$\Rightarrow 8 = 2x$
$\Rightarrow x = \dfrac{8}{2} = 4$
$\therefore$ Binita's present age = 4 yrs.
$\Rightarrow$ Savita's present age = $4 + 4 = 8$ yrs.
$\Rightarrow$ Binita's present age 16 yrs hence = $16 + 4 = 20$ yrs. Ans
$\Rightarrow$ Savita's present age 16 yrs hence = $16 + 8 = 24$ yrs. Ans
$\therefore$ Required ratio = $\dfrac{24}{20} = \dfrac{6}{5} = 6:5$ Ans
$\therefore$ Savita's age = $x + 4$
$\Rightarrow$ Savita's age after 16 yrs = $3(x + 4) = 3x + 12$
So, we have the equation:
$\Rightarrow (x + 4) + 16 = 3x + 12$
$\Rightarrow x + 20 = 3x + 12$
$\Rightarrow 20 - 12 = 3x - x$
$\Rightarrow 8 = 2x$
$\Rightarrow x = \dfrac{8}{2} = 4$
$\therefore$ Binita's present age = 4 yrs.
$\Rightarrow$ Savita's present age = $4 + 4 = 8$ yrs.
$\Rightarrow$ Binita's present age 16 yrs hence = $16 + 4 = 20$ yrs. Ans
$\Rightarrow$ Savita's present age 16 yrs hence = $16 + 8 = 24$ yrs. Ans
$\therefore$ Required ratio = $\dfrac{24}{20} = \dfrac{6}{5} = 6:5$ Ans
Q13. In 1991, Amrit's age is 8 years. His elder brother Prakash is 14 years elder than him. Find Prakash's age and the year in which he was born. Also, find the ratio between their age in the year 2020.
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$\Rightarrow$ Let Prakash's age in 1991 be = $x$ yrs
$\Rightarrow$ Given, Amrit's age in 1991 = 8 yrs
$\Rightarrow$ Given, difference between the age = 14
$\therefore$ Prakash's age in 1991 = $x- 8 = 14$
$\Rightarrow x = 14 + 8$
$\Rightarrow x = 22$
As such, Prakash's age in 1991 was = 22 yrs Ans
$\therefore$ Prakas's birth-year = $1991 - 14 = 1969$ Ans
For the year 2020:
$\Rightarrow$ No. of years between 1991 and 2020 = $2020 - 1991 = 29$ yrs
$\therefore$ Prakash's age in 2020 = $22 + 29 = 51$ yrs
$\Rightarrow$ And, Amrit's age in 2020 = $29 + 8 = 37$ yrs
$\therefore$ Required ratio = $\dfrac{51}{37} = 51:37$ Ans
$\Rightarrow$ Given, Amrit's age in 1991 = 8 yrs
$\Rightarrow$ Given, difference between the age = 14
$\therefore$ Prakash's age in 1991 = $x- 8 = 14$
$\Rightarrow x = 14 + 8$
$\Rightarrow x = 22$
As such, Prakash's age in 1991 was = 22 yrs Ans
$\therefore$ Prakas's birth-year = $1991 - 14 = 1969$ Ans
For the year 2020:
$\Rightarrow$ No. of years between 1991 and 2020 = $2020 - 1991 = 29$ yrs
$\therefore$ Prakash's age in 2020 = $22 + 29 = 51$ yrs
$\Rightarrow$ And, Amrit's age in 2020 = $29 + 8 = 37$ yrs
$\therefore$ Required ratio = $\dfrac{51}{37} = 51:37$ Ans