One application of linear equations is what are termed age problems. When solving age problems, generally the age of two different people (or objects) both now and in the future (or past) are compared. The objective of these problems is usually to find each subject’s current age. Since there can be a lot of information in these problems, a chart can be used to help organize and solve. An example of such a table is below.
Joey is 20 years younger than Becky. In two years, Becky will be twice as old as Joey. Fill in the age problem chart, but do not solve.
Using this last statement gives us the equation to solve: B + 2 = 2 ( B − 18)
Carmen is 12 years older than David. Five years ago, the sum of their ages was 28. How old are they now?
Filling in the chart gives us:
The last statement gives us the equation to solve: Five years ago, the sum of their ages was 28 Therefore, Carmen is David’s age (13) + 12 years = 25 years old.
The sum of the ages of Nicole and Kristin is 32. In two years, Nicole will be three times as old as Kristin. How old are they now?
Filling in the chart gives us:
The last statement gives us the equation to solve: In two years, Nicole will be three times as old as Kristin If Nicole is 25 years old, then Kristin is 32 − 25 = 7 years old.
Louise is 26 years old. Her daughter Carmen is 4 years old. In how many years will Louise be double her daughter’s age?
Filling in the chart gives us:
The last statement gives us the equation to solve: In how many years will Louise be double her daughter’s age? In 18 years, Louise will be twice the age of her daughter. For Questions 1 to 8, write the equation(s) that define the relationship.
Solve Questions 9 to 20.
Answer Key 7.9
Problems on ages is an important chapter for SSC/Banking and all other exams. In SSC Prelims 2 to 3 questions are asked and in mains 4 to 5 questions can be asked on this topic. As most of the questions on this topic of this chapter can be solved by analytical thinking. So, it plays a crucial role in the examination. Sometimes the question asked are confusing and complicated, so we have to learn the concept well to easily score marks for these types of questions. Table of Contents: 1. Problems on ages :- basics and concept 2. Useful tips and tricks to solve the problems of ages 3. Important Formulas 4. Sample Questions – problems on ages 1. Problems on ages – basics and concept In the quantitative aptitude section( banking /SSC exams) the problems on ages are kind of brain teasers, at the very first time when a candidate studies this it may seem to be complex, but it becomes easy when solved step by step. In the quantitative aptitude sector problems on ages mostly are asked for 2-3 marks but there may be a possibility of age-based questions being asked as a part of the data sufficiency or data interpretation. So it is very important to clarify the concept to each and every candidate. 2. Useful tips and tricks to solve the problems of ages The useful tips given below are for the Candidates who are not much familiar with the concept and tendency to skip the problems on ages or answer them incorrectly. These tips may help you to clear the concept and answers the questions correctly. I) To read the question carefully and gradually form the equation is the most important thing. It helps you answer the question. II) Basic things like subtraction, addition, multiplication, and division will help a candidate reach the answer and no complicated calculations are required to answer these questions. III) Arrange the values correctly and use them as linear equations. IV) Once the linear equation has been formed, solve the equation to find the answer. V) The final step is to recheck the answer obtained by placing it in the equation formed to ensure that no error has been made while calculating. The ‘problems on ages’ is one such topic which is not just asked in the preliminary phase of the examination but questions from this topic may also be asked in the main examination in a rather complex manner. 3. Important Formulas The formulas given below are related to the problems on ages which may help you to answer the problems quicker and also get a better idea of the concept:- I) Suppose if the present age of a person is x, then after n years, the age of the person will be (x+n) years. II) Suppose if the present age of a person is x, then before n years the age of the person will be (x-n) years. III) Suppose the ratio of two persons is p : q, then their age will be px and qx respectively. IV) Suppose the present age of a person is x, then n times the present age will be (x * n) years V) Suppose the present age of a person is x, then 1/n of the age shall be equal to (x/n) years These formulas and tricks will help you in solving the questions easily and more efficiently. 4. Sample Questions – problems on ages 1. Question A) 13 years B) 16 years C) 8 years D) 19 years E) None of these Answer:- D Let the age of Amit and Neha five years ago 8x and 7x respectively. Amit’s present age = (8x + 5) Neha’s present age = (7x + 5) Now, as per the equation, {(8x + 5) + 3} /{( 7x + 5) + 3} = 12/11 => 88x + 88 = 84x + 96 => 4x = 8 ⇒ x = 2. ∴ Neha’s present age = (7x + 5) = (7 × 2 + 5) = 19 years. Hence, option D is correct. Tricks:- Amit : Neha = 8 : 7 ( -5) = 12 : 11 (+3) = ( – 5 + 3 ) = 2 So, Neha’s age = 7 × 2 = 14 Neha’s present age = 14 + 5 = 19 years Or, Neha’s age = 11 × 2 = 22 Neha’s present age = 22 – 3 = 19 years 2.Question A) 42 years B) 64 years C) 70 years D) 67 years E) None of these Answer:- B Let the present age of three friend’s are = 3x, 5x and 7x (3x – 8) + (5x – 8) + (7x – 8) = 96 15x – 24 = 96 15x = 120 x = 8 Their present ages are 24 years, 40 years and 56 years respectively.The sum of the present ages of the first two friends = ( 24 + 40) = 64 years Hence, option B is correct. 3. Question A) 1 : 3 B) 2 : 3 C) 3 : 4 D) 5 : 3 E) None of these Answer – D Let the present ages of Father and son-in-law be 9x and 5x respectively. 9x × 5x = 1125 45×2 = 1125 x2 = 25 x = 5. Required ratio = (9x + 5) : (5x + 5) ⇒ 50 : 30 ⇒ 5 : 3. Hence, option D is correct. 4. Question A) 23 years B) 32 years C) 21 years D) 33 years E) None of these Answer:- A Let the ages of Aman, Nageshwar and Satyam 5 years ago be 2x, 3x and 4x years respectively. So, total of their present ages will be, (2x + 5) + (3x +5) + (4x + 5) = 96=> 9x + 15 = 96=> 9x = 81 x = 9. So, the present age of Aman =( 2x + 5 )=( 2 × 9 + 5 )= 23 years. Hence, option A is correct. 5. Question A) 1 : 3 B) 3 : 4 C) 2 : 3 D) 3 : 5 E) None of these Answer :-. B Assume 2x and 3x be the present age of two friends respectively. Then, 2x – 6 = 1 3x – 63⇒ 6x – 18 = 3x – 6 ⇒ 3x = 12 ⇒ x = 4. So, required ratio = (2x + 4) : (3x + 4) ⇒ 12 : 16 ⇒ 3 : 4. Hence, option B is correct. Tricks :- 2 : 3 —– ( × 2) = 4 : 6 (× 2) = 8 : 12 1 : 3 —– ( × 1) = 1 : 3 ( × 2) = 2 : 6 So, the present ages of the two boys 8 years and 12 years respectively. 4 years later their ages will be (8+4) = 12 years and (12+4)= 16 years. Ratio = 12 : 16 = 3 : 4. 6. Question A) 33 years B) 36 years C) 40 years D) 26 years E) None of these Answer:-. A Let, the present age of daughter = p Present age of her mother = 2p 10 yr back, the ratio of their ages was = 12: 1 So, (2p – 10)/(p – 10) = 12 /1=> 2p – 10 = 12p – 120=> 10p = 110 => P = 110/10 = 11 Present age of daughter = 11 years Present age of mother = 11× 2 = 22 years Thus, the sum of the present age of mother and her daughter = 22+11 yrs= 33 years Here , A is the correct answer. Tricks :- Mother : Daughter = 2 : 1 (× 11) = 22 : 11 = 12 : 1 ( × 1) = 12 : 1 Present age of Mother = 22 years Present age of Daughter = 11 years Thus, Sum of their ages = 22 + 11 = 33 years. 7. Question A) 20 yearsB) 22 earsC) 15 yearsD) 13 years E) 21 years Answer: A Let the present age of Chetan = x years So, Bikash’s present age = 2x And Amit’s present age = 2x + 2 According to the question, x+2x+2+2x = 52 ⇒5x+2 = 52 ⇒5x=50 ⇒x=10 So, Bikash’s age = 2×10 = 20 years 8. Question A) 12 years, 41 years B) 15 years, 53 yearsC) 11 years, 34 yearsD) 12 years, 44 years E) 21 years, 42 years Answer: D Solution: Let the present age of the elder brother = x years The present age of the younger brother = y years According to the question, After 4 years, age of the elder brother = x+4 after 4 years the age of younger brother = y+4 So, x+4 = 3 (y+4) ———–(2) x+4 = 3y + 12 From the equation (1) we get, Now putting the value of x in equation 2, we get (56-y) + 4 = 3y + 12 ⇒60 – y = 3y + 12 ⇒y = 12 So, the younger brother’s present age is =12 years the elder brother’s present age = 56-12 = 44 years Here the correct answer is D. 9. Question A) 36 yearsB) 24 yearsC) 27 yearsD) 18 years E) 22 years Answer:- BExplanation:-Let the present age of Akash = x yearsand he is younger to Ketan by y years Then, Ketan’s age = (x + y) years Vijay’s age = (x – y) years Now, according to the question,Sum of ages of Ketan and Vijay = 48(x + y) + (x – y) = 482x = 48 years x = 24 years Hence, present age of Akash is 24 yr. 10. Question A) 60 yearsB) 55 yearsC) 75 yearsD) 50 years E) none of these Answer :- A 15 years later, ratio between your uncle and your age = 2 :1 Now,(3x + 15)/(x + 15) = 2/1=> 3x + 15 = 2x + 30 => x = 15 Thus, Sum of the ages of your uncle and your = ( 3x + x )= 4 × 15 = 60 years Here the correct answer is A . 11. Question A) 45 years, 9 yearsB) 55 years, 11 yearsC) 65 years, 13 yearsD) 40 years, 8 years E) 50 years, 10 years Answer :- E Then, present age of Kamal = 5x years After 10 years, According to the question, (5x + 10)/(x + 10) = 3/1=> 5x + 10 = 3x + 30=> 2x = 20 => x = 10 Present age of Shiva = 10 years 12. Question A) 35 years, 12.5 years B) 33 years, 11 years C) 45 years, 16 years D) 50 years, 18.5 years E) None of these Answer:-A Explanation:- Let the present ages of Sanjay and Vikram be x years and y years, respectively. According to the question, (x – 5)/( y – 5) = 4/1=> x – 5 = 4y – 20 => x = 4y – 15 —————–(1) 10 years later,( x + 10)/(y + 10) = 2 : 1=> x + 10 = 2y + 20 => x = 2y + 10 —————-(2) Equating both the equations (1) and (2) ,we get, 4y – 15 = 2y + 10=> 2y = 25 => y = 12.5 Putting the value of y in equation (2),we get, x = 2 × 12.5 + 10 Thus,the present age of Sanjay = 35 years 13.Question (a) 16 yrs(b) 20 yr (c) 15 yr (d) 24 yr (e) 8 yr Answer :-A 4 years ago, let, Raman’s age = x years And Sharma’s age = 3x/4 years Now, Present age of Raman = x + 4 years According to the question, 5/6 ( x + 4 + 4) = (3x/4 + 4 + 4)=> 5/6 ( x + 8) = ( 3x/4 + 8)=> 4(5x + 40) = 6( 3x + 32)=> 20x + 160 = 18x + 192=> 2x = 32 => x = 16 Thus the present age of Sharma =( 3/4 × 16 + 4) years= 16 years Here the correct answer is A. 14. Question (a) 3 (b) 4 (c) 6 (d) 8 (e) none of these Answer :-C According to the question,(36 + p)/( 50 + p) = 3/4=> 144 + 4p = 150 + 3p=> p = 6 Thus, the value of p = 6. 15. Question (a) 7:4 (b) 4:7 (c) 11:8 (d) 10 : 7 (e) None of the above Answer :- D Ratio = (48 – 8) : (36 – 8) = 40 : 28 = 10 : 7 Here the correct answer is D. 16. Question (b) 11 yr (d) 10 yr (a) 12 yr (c) 10.5 yr Answer :- A Explanation :- Total age of two teachers and total age of two teachers and students together = 27 x 3 = 81 yr : Age of the student = 81-70 = 11 yr 17.Question (a) 30 yr (b) 34 yr (c) 32 yr (d) 40 yr (e) None of the above Answer :- C Explanation :- Total age of Saikat and Shivani = 36 × 2 = 72 yr Let age of Shivani = x yr Then, age of Saikat = (x + 8) yr According to the question, x+x+8 = 72 2x = 64 x = 32 Hence, Shivani’s present age = 32 years 18. Question The ratio between the present ages of Irfaan and Kapil is 3 : 8. After 8 years, Irfaan’s age will be 20 yr. What was Kapil’s age 5 years hence? (a) 37 yr (b) 27 yr (c) 28 yr (d) 38 yr Answer :-A 3x years and 8x years respectively. 3x + 8 = 20 => 3x = 12 x = 4 Kapil’s present age = 8x = 8×4 = 32 years Hence, Kapil’s age 5 years hence = 32+5 = 37 years 19. Question (a) 11 yr (b) 13 yr (c) 19 yr (d) 18 yr (e) None of the above Answer :- C Let Tanmay and Vivek’s ages are 3x yr and 7x yr, respectively.7x + 4 = 39 ⇒ x = 5=3×5-4=11 yrHence, Tanmay’s age 4 yr later= 3×5 + 4 = 19 years. 20. Question The average age of a group of five girls is 24. If the present age of the youngest girl is 8 year, what was the average age of the group at the time of the birth of the youngest girl? (b) 16 yr (d) 18 yr (a) 22 yr (c) 12 yr (e) 20 yr Answer:- E Explanation:- Total age of the group of five girls = 24 x 5 = 120 Total age of four girls at the time of birth of youngest girl=( 120 – 8×5) years = 120 – 40 = 80 years Hence, required average age = 80/4 = 20 yr Hence the correct answer is E. 21. Question (a) 84 yr (b) 70 yr (c) 40 yr (d) 35 yr Answer:- C Explanation:- Let the present age of Rahul = x. Then, present age of Rahul’s mother= 4x Now, 5 yr ago, Rahul’s mother’s age = 7 x Rahul’s age 4x -5= 7(x – 5) => 4x – 5 = 7x – 35 =>3x = 30 =>x = 10 .. Rahul’s present age = x= 10 years .. Rahul’s mother’s present age= 4x 22. Question (a) 3 (b) 1 (c) 1.5 (d) 2 (e) None of the above Answer :-B Explanation:- Let Arvind’s age = x yr Then, Prakash’s age = 3x yr According to the question, 3x + 7 = 2(x + 7) 3x + 7 = 2x + 14 X = 7 :: Age of Arvind after 14 yr = 7+ 14 = 21 yr Prakash’s present age = 21 yr Hence, 23. Question 10 years ago, the ratio of ages of a man and a woman was 13:17. After 17 years from now, the ratio of their ages will be 10:11 . What is the present age of the woman? (a) 23 yr (b) 40 yr (c) 27 yr (d) 44 yr (e) None of the above Answer:-C Explanation:- Let the ages of man and woman 10 yr before were 13x yr and 17x yr, respectively. Then, present age of man = 13x + 10 and present age of woman = 17x + 10 According to the question, (13x + 10 + 17)/(17x + 10 + 17) = 10/11 => (13x + 27)/(17x + 27) = 10/11 => 143x + 297 = 170x + 270 => 27x = 27 => x = 1 Hence ,the present age of the woman 24.Question (b) 18 yr(d) 30 yr(a) 26 yr(c) 42 yr (e) None of the above Answer:- E Explanation:-Let Shekhar’s present age = x yrThen, Kailash’s present age = 2x yrAccording to the question,(2x + 8)/(x + 8 ) = 22/1326x + 104 = 22x + 1764x = 72x = 18 Hence, Kailash’s age = 2 x 18 = 36 yr 25.Question (a) 56 yr (b) 63 yr (c) 70 yr (d) 77 yr (e) none of these Answer:- D Explanation:- Let, 7 yr ago, ages of P and Q were 4x years and 5x years, respectively. Then, present age of P = 4x + 7 Now, according to the question, (4x + 7+ 7)/(5x +7+7) =5/6 24x + 84 = 25x + 70 x = 14 Hence, Q’s present age =(5x + 7) = 5×14 + 7 years = 77 years. Hence the correct answer is D. Article Tags : |