2 2 9 8 4 7

# AGES

## AGES SET-9

1. A person’s present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the  age of his mother. How old is the mother at present ?A) 40 yearsB) 41 yrsC) 42 yrsD) 43 yrsAns. ALet the mother’s present age be x years.Then, the person’s present age = 2 x years.5   2 x + 8 = 1 (x + 8)5 2   2(2x + 40) = 5(x + 8)  x = 40 2.The age of father 10 years ago was thrice the age of his son. Ten years hence, father’s age will be twice  that of his son. The ratio of their present ages is :A) 7 : 3B) 13 : 4C) 9 : 2D) 5 : 2Ans. ALet the ages of father and son 10 years ago be 3x and x years respectively.Then, (3x + 10) + 10 = 2[(x + 10) + 10]  3x + 20 = 2x + 40  x = 20.  Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3 3. Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of  Ronit’s age. After further 8 years, how many times would he be of Ronit’s age ?A) 2 timesB) 3 timesC) 4 timesD) 5 timesAns. ALet Ronit’s present age be x years. Then, father’s present age =(x + 3x) years = 4x years.  (4x + 8) = 5 (x + 8)2   8x + 16 = 5x + 40  3x = 24  x = 8. Hence, required ratio = (4x + 16) = 48 = 2.(x + 16) 24 4. A person’s present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at presentA) 38B) 40C) 42D) 44Ans. BLet the mother’s present age be x years.Then, the person’s present age = (2/5 x) years. => (2/5 x + 8/2) = 1 (x + 8) => 2(2x + 40) = 5(x + 8) => x = 40 5. The sum of the present ages of a father and his son is 60 years. Six years ago, father’s age was five times the age of the son. After 6 years, son’s age will beA) 15 yearsB) 18 yearsC) 20 yearsD) 22 yearsAns. CHINT:(60 – x) – 6 = 5(x – 6)

## AGES SET-8

1. The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is :A) 31 kgB) 21 kgC) 35 kgD) 30 kgAns. ALet A, B, C represent their respective weights. Then, we have:A + B + C = (45 x 3) = 135 …. (i)A + B = (40 x 2) = 80 …. (ii)B + C = (43 x 2) = 86 ….(iii)Adding (ii) and (iii), we get: A + 2B + C = 166 …. (iv)Subtracting (i) from (iv), we get : B = 312. A pupil’s marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class is :A) 40B) 41C) 42D) 43Ans. ALet there be x pupils in the class.Total increase in marks = x x 1 = x2 2    x = (83 – 63)    x = 20       x= 40.2 2 3. The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team ?A) 21 yrsB) 22 yrsC) 23yrsD) 24 yrsAns. CLet the average age of the whole team by x years.  11x – (26 + 29) = 9(x -1)  11x – 9x = 46  2x = 46  x = 23.So, average age of the team is 23 years 4. The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is :A) 50 yrsB) 35 yrsC) 45 yrsD) 40 yrsAns. DSum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.Sum of the present ages of wife and child = (20 x 2 + 5 x 2) years = 50 years.  Husband’s present age = (90 – 50) years = 40 years 5. The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years) :A) 20, 35, 45B) 16, 28, 36C) 8, 20, 28D) None of the aboveAns. BLet their present ages be 4x, 7x and 9x years respectively.Then, (4x – 8) + (7x – 8) + (9x – 8) = 56  20x = 80  x = 4.  Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively

## AGES SET-7

1. Average age of A and B is 24 years and average age of B, C and D is 22 years. The sum of the ages of A, B, C and D isA) 90B) 98C) 120D) Data is not adequateAns. D 2. Total of the ages of A, B ahd C at present is 90 years. Ten years ago, the ratio of their ages was 1: 2: 3. What is the age of B at presentA) 25B) 30C) 45D) 60Ans. BLet their ages 10 years ago is x, 2x and 3x years. 10 + 2x + 10 + 3x + 10 = 90 hence x= 10 B?s present age = (2x + 10) =30 years 3. A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son isA) 20 yearsB) 21 yearsC) 22 yearsD) 24 yearsAns. CLet the son’s present age be x years. Then, man’s present age = (x + 24) years=> (x + 24) + 2 = 2(x + 2)=> x + 26 = 2x + 4So, x = 22 4. A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of this son isA) 21 yearsB) 22 yearsC) 23 yearsD) 24 yearsAns. BLet’s Son age is x, then Father age is x+24.=> 2(x+2) = (x+24+2)=> 2x+4 = x+26=> x = 22 years 5. Tanya’s grandfather was 8 times older to her 16 years ago. He would be 3 times of her age 8 years from now. What was ratio of ages of Tanya and her grandfather 8 years ago.A) 11:50B) 11:51C) 11:53D) 11:54Ans. CLet, Tanya age 16 years ago = x, Grandfather’s age 16 years ago = 8x. 8 years from now, 3(x+16+8) = (8x+16+8)=> x = 48/5 8 years ago ratio was: =>x+88x+8=485+88×485+8=>x+88x+8=485+88×485+8=>x+88x+8=485+88×485+8   =>88424=1153=>88424=1153=>88424=1153

## AGES SET-6

1. Sachin was twice as old as Ajay 10 years back. How old is Ajay today if Sachin will be 40 years old 10 years henceA) 18B) 25C) 15D) 20Ans. DSachin’s age today = 30 years. Sachin’s age 10 years back = 20 years. Ajay’s age 10 years back = 10 years. Ajay’s age today =20 years 2. In 10 years, A will be twice as old5as B was 10 years ago. If A is now 9 years older than B, the present age of B isA) 35B) 37C) 39D) 41Ans. CLet B’s age = x years. Then, As age = (x+ 9) years. (x+9+10)=2(x?10) hence x=39. Present age of B = 39 years 3. Ten years ago A was half of B in age. If the ratio of their present ages is 3 : 4, what will be the total of their present agesA) 30B) 35C) 37D) 41Ans. BLet A’s age 10 years ago = x years. Then, B’s age 10 years ago = 2x years.(x + 10) / (2x+ lO) = 3/4 => x = 5.So, the total of their present ages =(x + 10 + 2x + 10) = (3x + 20) = 35 years. 4. Sushil was thrice as old as Snehal 6 years back. Sushil will be times as old as Snehal 6 years hence. How old is Snehal todayA) 12B) 16C) 18D) 24Ans. ALet Snehals age 6 years back = x. Then, Sushils age 6 years back = 3x. (5/3) * (X + 6 + 6) = (3X + 6 + 6) So 5(x+ 12) = 3(3x+ 12),so x=6. Snehal Age = (x+ 6) years = 12 years 5. Six years ago, the ratio of the ages of Kunal and Sagar was 6:5, Four years hence, the ratio of their ages will be 11:10. What is Sagar age at presentA) 10 yearsB) 12 yearsC) 14 yearsD) 16 yearsAns. DLet six years ago the age of Kunal and Sagar are 6x and 5x resp.then, =>(6x+6)+4(5x+6)+4=1110=>(6x+6)+4(5x+6)+4=1110=>(6x+6)+4(5x+6)+4=1110 <=>10(6x+10)=11(5x+10)<=>10(6x+10)=11(5x+10)<=>10(6x+10)=11(5x+10) <=>5x=10=>x=2<=>5x=10=>x=2<=>5x=10=>x=2 So Sagar age is (5x+6) = 16

## AGES SET-5

1. Ten years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present agesA) 35B) 34C) 45D) 25Ans. ALet the present age of P and Q be 3x and 4x respectively.Ten years ago, P was half of Q in age=> 2(3x ? 10) = (4x ? 10) => 6x ? 20 = 4x ? 10 => 2x = 10 => x = 5 2. The total age of A and B is 12 years more than the total age of B and C. C is how many year younger than AA) 11B) 12C) 13D) 14Ans. BGiven that A+B = 12 + B + C=> A ? C = 12 + B ? B = 12=> C is younger than A by 12 years 3. The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder personA) 15B) 20C) 25D) 30Ans. DLet’s take the present age of the elder person = x and the present age of the younger person = x ? 16(x ? 6) = 3 (x-16-6)=> x ? 6 = 3x ? 66=> 2x = 60=> x = 60/2 = 30 4. The ages of two persons differ by 20 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectivelyA) 20,20B) 20,10C) 25,15D) 30,10Ans. DLet their ages be x and (x + 20) years. 5 (x – 5) = (x + 20 – 5) or 4x = 40 or x = 10. Their present ages are 30 years and 10 years5. Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 26 years. What is Deepak present age.A) 14B) 15C) 20D) 22Ans. BPresent age is 4x and 3x,=> 4x + 6 = 26 => x = 5 So Deepak age is = 3(5) = 15

## AGES SET-4

1. Raju age after 15 years will be 5 times his age 5 years back, What is the present age of RajuA) 15B) 14C) 10D) 8Ans. CExplanation:Clearly,x+15 = 5(x-5) <=> 4x = 40 => x = 10 2. Sachin is younger than Rahul by 7 years. If the ratio of their ages is 7:9, find the age of SachinA) 23.5B) 24.5C) 12.5D) 14.5Ans. BIf Rahul age is x, then Sachin age is x-7,so (x-7)/x = 7/9=> 9x-63 = 7x => 2x = 63=> x = 31.5 So Sachin age is 31.5 – 7 = 24.5 3. The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 yearsA) 7:8B) 7:9C) 3:8D) 5:8Ans. ALet P age and Q age is 6x years and 7x years.Then 7x – 6x = 4 <=> x = 4 So required ratio will be (6x+4): (7x+4) => 28:32 => 7:8 4. Ages of two persons differ by 16 years. If 6 year ago, the elder one be 3 times as old the younger one, find their present ageA) 12,28B) 14,30C) 16,32D) 18,34Ans. BLet the age of younger person is x,Then elder person age is (x+16)=> 3(x-6) = (x+16-6) [6 years before]=> 3x-18 = x+10=> x = 14.So other person age is x + 16 = 30 5. The sum of the ages of a father and son is 45 years. Five years ago, the product of their ages was four times the fathers age at that time. The present age of father and sonA) 34,11B) 35,10C) 36,9D) 40,5Ans. CLet sons age = x years. Then fathers age = (45 – x)years. (x?5)(45?x?5) = 4(45- x – 5) hence (x?5) = 4 so x = 9 Their ages are 36 years and 9 years.

## AGES SET-3

Q.1 Total age of some 7 years old & some 5 years old children is 60 yrs. If a team is to be selected from these children such that their total age is 48 years, in how many ways can it be done ? A) 2 B) 3C) 4D) 1Ans. D7*4+5*4=28+20=48 Q.2 At present ages of a father & his son are in the ratio of 7:3 & they will be in the ratio of 2 : 1 after 10 years. Then the present age of father is : A) 77 B) 56 C) 70 D) 42 Ans. C Shortcut:Father’s age = x*t (a-b)/ difference of cross productOr x =7t=10a=2b=1therefore,7*10(2-1)/1=70 Q.3 The present ages of A and B are in the ratio 2 : 3 and the ages of A and C are in the ratio 3 : 4. If the sum of the present ages of A, B and C is 92 years, how many years will it take by B and C to get their ages in the ratio 10 : 9? A) 2 B) 4 C) 5 D) 6 Ans. B A : B = 2 : 3 = 6 : 9 (Note: In this since A is common that’s why we have multiplied “2 with 3” & “3 with 9”) A : C = 3 : 4 = 6 : 8 (Multiplied “3 with 2” & “4 with 2”) ? A : B : C = 6 : 9 : 8 ? A age = × 92 = 24 yearsB age = × 92 = 36 years C = × 92 = 32 years After x years, = ? x = 4 years Q.4 The sum of ages of a son & father is 56 years. After 4 years, the age of father will be three times that of the son. Their ages respectively are A) 12 & 44 yrs B) 16 & 42 yrs C) 16 & 48 yrs D) 18 & 36 yrs Ans. A Shortcut:Son’s age=S1+t2(N-1)/N+1 [When age is in years ago] But in this question use this formula because [It is given after years] Son’s age= S1-t2(N-1)/N+1 Therefore,Son’s age is 56-4*2/4=12 where N= 3 as it is given three times Now, for father’s age= It is given in Question ,the sum of ages of a son & father is 56 years Then,12 + father’s age = 56 Father’s age = 56-12= 44 Other explanation: Suppose the age of father be a yrsThen the age of the son = (56-a)After four yrs the age of the father would be (a+4) yrs & the age of the son would (56-a+4)Now (a+4) = 3(56-a+4)(a+4) = 180 – 3aa = 44 yrsSo, the age of father = 44 yrs& the age of son = 56-44= 12 yrs Q.5 The average age of three girls is 16 years. If their ages are in the ratio 4 : 5 : 7, the age of the youngest girl is : A) 21 B) 15 C) 16 D) 12 Ans. CLet the ages of three girls be 4x, 5x, 7x (ratio 4 : 5 : 7 is given)Average age of the three girls = 16 yearsAverage age = = 1616x = 16 3x = 3.Age of the youngest girl = 4x = 4 3 = 12 years. Q.6 The ratio of the ages of two persons (A and B) is 2 : 3 and that of (B and C) is 4 : 5. If the average age of all the three is 35 years. What is B’s age? A) 24 B) 36 C) 40 D) 30 Ans. B Total age of A + B + C = 35 × 3 = 105= ? A = = ? C = ? + B + = 105? B = 36 years.

## AGES SET-2

Q.1 Ratio of the ages of the father & the son at present is 6:1. After 5 years ratio will become 7:2. What is the present age of the son ?   A) 30 yrs   B) 31 yrs   C) 32 yrs   D) 33 yrs   Ans. A   Sons’s age = Y * T(a-b) / difference of cross product   Or  1 * 5 (6-1) / 12 – 7   5*5 / 5 = 5 yrs   Father’s age = X *T (a-b) / Difference of cross product   6*5 (6-1) / 12-7   =6*5 = 30 yrs   Q.2 10 yrs back sum of the ages of a mother & her daughter is 45. If the ratio of their present ages be 9:4. Then the present age of the daughter is :-   A) 20 yrs   B) 21 yrs   C) 22 yrs   D) 23 yrs   Ans. A   10 yrs back, D + M = 45   Now, at present, D + M =45+10 = 55   Thus, 9x+4x=55   13x=55       Or x=5   Or D=4x = 20   Q.3 Suresh’s father is 2yrs older than his mother. His age is 3yrs less than half of his mother ago. He was born when his father was 23yrs old. Find the age of Suresh ?   A) 14yrs   B) 15yrs   C) 16yrs   D) 17 yrs   Ans. A   F = 2 + M   M = F – 2   Or S = M/2 – 3   F-2/2 – 3   Or F-8/2   Or F = S+23   = 23 + F-8/2   Or F = 37+F / 2   F = 37   Now, Suresh’s age = 37-23 = 14 yrs   Q.4 Three years earlier father was 7 times as old as his son. Three years hence, father’s age would be four times that of his son. What is the present age of son ?   A) 9 yrs   B) 10 yrs   C) 11 yrs   D) 12 yrs   Ans. A   Shortcut:   T2(z-1) + T1(x-1)   3(4-1)+3(7-1) / 7-4   = 9yrs Q.5 Peter is twice as old as Paul was when Peter was as old as Paul is now. The combined age of Peter and Paul is 42years. How old is peter now?   A) 21   B) 28   C) 24   D) 26   Ans. B     peter’s age = x   paul’s age = y   x+y =42   Since, x=2y, then x+2y=42 3y = 42 y=14 i.e. Paul’s age   Or Peter’s age = 28 years

## AGES SET-1

Q.1 Present ages of Anu and Raj are in the ratio 4:5. Eight years from now the ratio of their ages will be 5:6. Find the present age of Raj ?   A) 38   B) 39   C) 40   D) 41   Ans. C   Let the present ages of Anu and Raj be 4x years and 5x years respectively. After eight years. Anu’s age = (4x + 8) years; After eight years, Raj’s age = (5x + 8) years. Therefore, the ratio of their ages after eight years = 4x + 8 /  5x + 8 This is given to be 5 : 6 Therefore, 4x + 8/ 5x + 8 = 5/6 Cross-multiplication gives 6 (4x + 8) = 5 (5x + 8) or 24x + 48 = 25x + 40 or 24x + 48 – 40 = 25x or 24x + 8 = 25x or 8 = 25x – 24x or 8 = x Therefore, Anu’s present age = 4x = 4 × 8 = 32 years Raj’s present age = 5x = 5 × 8 = 40 years   Q.2 A grandfather is ten times older than his granddaughter. He is also 54 years older than her. Find their present age of Grandfather ?   A) 50 yrs   B) 60 yrs   C) 61 yrs   D) 62 yrs   Ans. B   Let the granddaughter’s age be x years. Therefore, grandfather’s age will be 10x years. According to the question, Grandfather’s age = Granddaughter’s age + 54 years 10x = x + 54 Transposing x to L.H.S, we obtain 10x – x = 54 9x = 54 x = 6 Granddaughter’s age = x years = 6 years Grandfather’s age = 10x years = (10 × 6) years = 60 years   Q.3 10 yrs ago the sum of the ages of two brothers was equal to one-third of the age of their father. Elder brother is 2yrs older than the younger . At present the sum of their ages is less than the age of the father by 14yrs. What is the age of the father ? A) 46 yrs B) 47 yrs C) 48 yrs D) 49 yrs Ans. A Let the age of father, elder son & younger son be x,y & z yrs Therefore, y-10+z-10 = 1/3(x-10) Or 3y-30+3z-30 = x-10 Or –x+3y+3z = 50—–i y-z = 2—–ii x-(y+z) = 14 x-y-z = 14—-iii Multiply equation iii by 3 & then add equation I, we get 2x = 92 X=92/2 = 46   Q.4 The age of the father 3yrs ago was 7 times the age of his son. At present the father’s age is five times that of his son. What are the present ages of the father & the son ?   A) Father’s age=45 yrs , Son’s age=9 yrs   B) Father’s age=46 yrs , Son’s age=10 yrs   C) Father’s age=47 yrs , Son’s age=11 yrs   D) Father’s age=48 yrs , Son’s age=12 yrs   Ans. A   Shortcut:   Sons’s age = T1 (x-1) / (x-y)   18/2 = 9 yrs   In the same way, we have   Father’s age = 45 yrs   Q.5 Sum of the ages of the mother & her daughter is 50 yrs. Also 5 yrs ago, the mother’s age was 7 times the age of the daughter. What are the present ages of the mother & the daughter ?   A) Mother’s age= 40 yrs. & Daughter’s age= 9   B) Mother’s age= 41 yrs. & Daughter’s age= 10   C) Mother’s age= 40 yrs. & Daughter’s age= 10   D) Mother’s age=39 & Daughter’s age=10 yrs.   Ans. C   Shortcut:   Daughter’s age = S1+T1 (N1-1) / N1+1   50+ 5(7-1) / 7+1   10 yrs   Or Mother’s age = 50-10 = 40 yrs   NOTE: If there will be after…….years like”after 5 years” in place of ago like “5 yrs ago”, then use this formula:   S1-T1(N-1) / N1+1