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For the following questions answer them individually
The sum of the ages of husband and wife at present is 100. Ten years ago the ratio of their ages was 9:7. What is the age of the husband?
Let husband's age = $$x$$ years
=> Wife's age = $$(100 - x)$$ years
According to ques,
=> $$\frac{x - 10}{100 - x - 10} = \frac{9}{7}$$
=> $$\frac{x - 10}{90 - x} = \frac{9}{7}$$
=> $$7x - 70 = 810 - 9x$$
=> $$9x + 7x = 810 + 70 = 880$$
=> $$x = \frac{880}{16} = 55$$ years
=> Ans - (B)
The average age of a jury of 5 is 40. If a member aged 35 resigns and man aged 25 becomes a member, then the average age of the new jury is
Initially, sum of ages of the jury = 200,
then man aged 35 resigns, sum of ages = 200-35
then man aged 25 joins, sum of ages = 200-35+25
Final number of members in the jury =5
So, average age of the jury = (200-35+25)/5 = 38
An employer reduces the number of employees in the ratio 8 : 5 and increases their wages in the ratio 7 : 9. As a result, the overall wages bill is
Let's say employees were change from 8x to 5x and wage per employee is changed from 7y to 9y
Hence total wage is changed from 56xy to 45xy or in a ratio of 56:45
The ratio of present ages of Ranjini and Shahid is 5:4. After 13 years the ratio of their ages will be 6:5. What is Ranjini's present age?
Let Ranjini's present age = $$5x$$ years and Shahid's present age = $$4x$$ years
According to ques, => $$\frac{5x + 13}{4x + 13} = \frac{6}{5}$$
=> $$25x + 65 = 24x + 78$$
=> $$25x - 24x = 78 - 65$$
=> $$x = 13$$
$$\therefore$$ Ranjini's age = $$5 \times 13 = 65$$ years
=> Ans - (B)
The ratio of present ages of Ratnabali and Shaukat is 8:5. After 22 years the ratio of their ages will be 10:9. At present, what is Ratnabali's age?
Let Ratnabali's present age = $$8x$$ years and Shaukat's present age = $$5x$$ years
According to ques, => $$\frac{8x + 22}{5x + 22} = \frac{10}{9}$$
=> $$72x + 198 = 50x + 220$$
=> $$72x - 50x = 220 - 198$$
=> $$22x = 22$$
=> $$x = \frac{22}{22} = 1$$
$$\therefore$$ Ratnabali's age = $$8 \times 1 = 8$$ years
=> Ans - (D)
The ratio of present ages of Ratna and Shantanu is 5:4. After 19 years the ratio of their ages will be 10:9. What is Ratna's present age?
Let Ratna's present age = $$5x$$ years and Shantanu's present age = $$4x$$ years
According to ques, => $$\frac{5x + 19}{4x + 19} = \frac{10}{9}$$
=> $$45x + 171 = 40x + 190$$
=> $$45x - 40x = 190 - 171$$
=> $$5x = 19$$
=> $$x = \frac{19}{5}$$
$$\therefore$$ Ratna's age = $$5 \times \frac{19}{5} = 19$$ years
=> Ans - (A)
The ratio of present ages of Ramya and Saurabh is 8:7. After 10 years the ratio of their ages will be 12:11. What is Ramya's present age?
Let Ramya's present age = $$8x$$ years and Saurabh's present age = $$7x$$ years
According to ques, => $$\frac{8x + 10}{7x + 10} = \frac{12}{11}$$
=> $$88x + 110 = 84x + 120$$
=> $$88x - 84x = 120 - 110 = 10$$
=> $$x = \frac{10}{4} = 2.5$$
$$\therefore$$ Ramys's age = $$8 \times 2.5 = 20$$ years
=> Ans - (A)
The ratio of present ages of Rangitha and Shaheen is 6:5. After 12 years the ratio of their ages will be 7:6. What is Rangitha's present age?
Let present age of Rangitha = $$6x$$ years
=> Present age of Shaheen = $$5x$$ years
According to question, => $$\frac{6x + 12}{5x + 12} = \frac{7}{6}$$
=> $$36x + 72 = 35x + 84$$
=> $$x = 84 - 72 = 12$$
$$\therefore$$ Rangitha's present age = $$6 \times 12 = 72$$ years
The brother is elder to his sister by 6 years. Seven years ago the product of their ages was 72. What is the age of the brother?
Let age of brother = $$x$$ years
=> Age of sister = $$(x - 6)$$ years
Product of their ages 7 years ago = $$(x - 7) \times (x - 13) = 72$$
=> $$x^2 - 13x - 7x + 91 - 72 = 0$$
=> $$x^2 - 20x + 19 = 0$$
=> $$x^2 - x - 19x + 19 = 0$$
=> $$x(x - 1) - 19(x - 1) = 0$$
=> $$(x - 1) (x - 19) = 0$$
=> $$x = 1 , 19$$
Since, $$x \neq 1$$, => Age of brother = 19 years
The ratio of ages of father and son is 7:2. Five years ago the product of their ages was 150. What is the age of the father?
Let father's age = $$7x$$ years and son's age = $$2x$$ years
According to ques, => $$(7x-5) (2x-5)=150$$
=> $$14x^2-35x-10x+25-150=0$$
=> $$14x^2-45x-125=0$$
=> $$14x^2-70x+25x-125=0$$
=> $$14x(x-5)+25(x-5)=0$$
=> $$(x-5)(14x+25)=0$$
=> $$x=5,\frac{-25}{14}$$
Since, age can't be negative, thus $$x=5$$
$$\therefore$$ Father's age = $$7 \times 5=35$$ years
=> Ans - (C)
The sum of the ages of father and son at present is 33. Two years ago the product of their ages was 28. What is the age of the father and the son?
Let the age of son = $$x$$ years and father's age = $$(33-x)$$ years
Product of their ages 2 years ago = $$(x-2)(33-x-2) = 28$$
=> $$(x-2)(31-x)=28$$
=> $$31x-x^2-62+2x=28$$
=> $$x^2-33x+90=0$$
=> $$x^2-3x-30x+90=0$$
=> $$x(x-3)-30(x-3)=0$$
=> $$(x-3)(x-30)=0$$
=> $$x=30,3$$
$$\therefore$$ Ages of father and son are 30 and 3
=> Ans - (B)
I am three times as old as my son. 15 years hence, I will by twice as old as my son. The sum of our ages is
Let's say son's age is $$x$$
hence father's present age will be $$3x$$
after 15 years son's age will be $$x+15$$ and father's age will be $$3x+15$$ and it is twice the age of son
so $$3x+15$$ = 2 ($$x+15$$)
solve for $$x$$
Ronald and Elan are working on an Assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take working together on two different computers to type an assignment of 110 pages ?
Ronald takes 6 hours to type 32 pages
no.of pages typed by ronald per hour = 32/6 = 16/3
Elan takes 5 hours to type 40 pages
no.of pages typed by elan per hour = 40/5 = 8
in 1hr, both can type 8+16/3 pages = 40/3
time taken by both to type 110 pages = 110/(40/3) = 33/4 = 8hrs 15mins ( $$\because$$ 1/4 hr = 15mins)
so the answer is option C.
The sum of the ages of husband and wife at present is 60. Four years ago the ratio of their ages was 7:6. What is the age of the husband?
Let present age of husband = $$x$$ years
=> Present age of wife = $$(60 - x)$$ years
Ratio of their ages 4 years ago = $$\frac{x - 4}{(60 - x) - 4} = \frac{7}{6}$$
= $$\frac{x - 4}{56 - x} = \frac{7}{6}$$
= $$6x - 24 = 392 - 7x$$
=> $$6x + 7x = 392 + 24 = 416$$
=> $$x = \frac{416}{13} = 32$$ years
The ratio of present ages of Rasika and Shami is 7:5. After 17 years the ratio of their ages will be 12:11. What is Rasika's present age?
Let Rasika's present age = $$7x$$ years and Shami's present age = $$5x$$ years
According to ques, => $$\frac{7x + 17}{5x + 17} = \frac{12}{11}$$
=> $$77x + 187 = 60x + 204$$
=> $$77x - 60x = 204 - 187$$
=> $$17x = 17$$
=> $$x = \frac{17}{17} = 1$$
$$\therefore$$ Rasika's age = $$7 \times 1 = 7$$ years
=> Ans - (D)
The ratio of present ages of Rangana and Sayed is 7:5. After 11 years the ratio of their ages will be 4:3. What is Rangana's present age?
Let Rangana's present age = $$7x$$ years and Sayed's present age = $$5x$$ years
According to ques, => $$\frac{7x + 11}{5x + 11} = \frac{4}{3}$$
=> $$21x + 33 = 20x + 44$$
=> $$21x - 20x = 44 - 33$$
=> $$x = 11$$
$$\therefore$$ Rangana's age = $$7 \times 11 = 77$$ years
=> Ans - (B)
The ratio of present ages of Ramita and Satyajit is 9:7. After 9 years the ratio of their ages will be 5:4. What is Ramita's present age?
Let Ramita's present age = $$9x$$ years and Satyajit's present age = $$7x$$ years
According to ques, => $$\frac{9x + 9}{7x + 9} = \frac{5}{4}$$
=> $$36x + 36 = 35x + 45$$
=> $$36x - 35x = 45 - 36$$
=> $$x = 9$$
$$\therefore$$ Ramita's age = $$9 \times 9 = 81$$ years
=> Ans - (A)
At present, the ratio of the ages of Maya and Chhaya is 6:5 and fifteen years from now, the ratio will get changed to 9:8. Maya's present age is
Let's say maya's age is $$6x$$ and chaya's age is $$5x$$.
after 15 years ages will be $$6x+15$$ and $$5x+15$$.
New ratio will be $$\frac{6x+15}{5x+15} = \frac{9}{8}$$.
After solving above equation we will get $$x$$ equals to 5
So maya's age will be 30.
The sum of the ages of brother and sister at present is 21. Five years ago the product of their ages was 28. What is the age of the brother and the sister?
Let the age of brother = $$x$$ years and sister's age = $$(21-x)$$ years
Product of their ages 5 years ago = $$(x-5)(21-x-5) = 28$$
=> $$(x-5)(16-x)=28$$
=> $$16x-x^2-80+5x=28$$
=> $$x^2-21x+108=0$ $
=> $$x^2-9x-12x+108=0$$
=> $$x(x-9)-12(x-9)=0$$
=> $$(x-12)(x-9)=0$$
=> $$x=12,9$$
$$ \therefore$$ Ages of brother and sister are 12 and 9
=> Ans - (A)
The sum of the ages of husband and wife at present is 56. Ten years ago the product of their ages was 320. What is the age of the husband and the wife?
Let husband's age = $$x$$ years
=> Wife's age = $$(56 - x)$$ years
According to ques, $$(x-10)(56-x-10)=320$$
=> $$(x-10)(46-x)=320$$
=> $$46x-x^2-460+10x=320$$
=> $ $x^2-56x+780=0$$
=> $$x^2-30x-26x+780=0$$
=> $$x(x-30)-26(x-30)=0$$
=> $$(x-30)(x-26)=0$$
=> $ $x=30,26$$
$$\therefore$$ Ages of the husband and the wife = 30 and 26 years
The ratio of present ages of Rambha and Sarvesh is 8:5. After 7 years the ratio of their ages will be 5:4. What is Rambha's present age?
Let Rambha's present age = $$8x$$ years and Sarvesh's present age = $$5x$$ years
According to ques, => $$\frac{8x + 7}{5x + 7} = \frac{5}{4}$$
=> $$32x + 28 = 25x + 35$$
=> $$32x - 25x = 35 - 28$$
=> $$7x = 7$$
=> $$x = \frac{7}{7} = 1$$
$$\therefore$$ Rambha's age = $$8 \times 1 = 8$$ years
=> Ans - (C)
A and B have to type a book together containing 120 pages. A takes 9 hrs to type 36 pages and B takes 5 hrs to type 40 pages. A typed first 60 pages alone and the last 60 pages were typed by A and B together. How much time (in hours) will be taken to type the complete book?
A takes 9 hrs to type 36 pages
=> A's efficiency = $$\frac{36}{9}=4$$ pages/hr
Similarly, B's efficiency = $$\frac{40}{5}=8$$ pages/hr
A typed first 60 pages alone, => Time taken to print 60 pages = $$\frac{60}{4}=15$$ hours
Similarly, time taken to print last 60 pages by A and B together = $$\frac{60}{(4+8)}=5$$ hours
$$\therefore$$ Total time taken to complete the book = $$15+5=20$$ hours
=> Ans - (B)
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