Friday, 11 March 2016

GMAT word problems - Problems on Ages

Aptitude Questions with Answers – Problems on Ages 11
11. The ratio of the present age of A and B is 1:2 and 5 years ago, the ratio of their ages was 1:3. What will be the ratio of their ages after 5 years?
a)2:3            b)4:7            c)3:5            d)7:8
Answer :C
Explanation: Let the present ages of A and B be x and 2x years respectively.
5 years ago, their ages were x-5 and 2x-5.
5 years ago, their ages were in the ratio of 1:3.
A’s age 5 years ago/ B’s age 5 years ago =
1 / 3
=>
x-5 / 2x-5
=
1 / 3
  =>3x-15=2x-5 =>x=10.
Their present ages are 10 and 20.
After 5 years, their ages will be 10+5 and 20+5 = 15 and 25
Ratio of their ages after 5 years =15:25 = 3:5

Quantitative Aptitude for CAT – Age related problems
12.The sum of the ages of 5 girls each both at 3 years intervals is 60 years. What is the age of eldest girl?
a)12 years  b)16 years      c)18 years     d)20 years
Answer: C
Explanation : Let the age of the youngest girl be x.
Then each both at 3 years interval, the ages will be x ,x+3, x+6, x+9 ,x+12 .
                   =>5x+30=60 >x=6.
   Therefore, age of the eldest girl= x+12 =6+12=18.

Aptitude Problems with Answers – Problems on Ages
13. A’s grandfather was 8 times older to him 16 years ago. His grandfather would be 3 times of his age 8 years from now. 8 years ago, what was the ratio of A ‘s age to that of his grandfather’s age?
a)53:11      b)12:47       c)11:53      d)19:21
Answer: C
Explanation : Let 16 years ago, A’s age be x and his grandfathers be 8x.
          Present age of A is x+16 and and grandfathers is 8x+16
        After 8 years,  A’s age will be  x+24 and his grandfather’s age will be 8x+24.
   After 8 years, grandfather will be 3 times of A.
 
Grandfather’s age after 8 years / A’s age after 8 years
=
3 / 1
                  
8x+24 / x+24
=
3 / 1
                =>8x+24=3x+72=> x=
48 / 5
  Ratio of their ages 8 years ago
=>x+8: 8x+8 =
48 / 5
+8  : 8 x
48 / 5
+ 8 = 11:53

GMAT Word Problems – Problems on Ages
14. At present age of the mother is 5 times that of the age of her daughter. After 3 years, age of the mother would be 4 times the age of her daughter. What is the age of the daughter after 3 years?
a)12 years     b)15 years      c)17 years      d)20 years
Answer : A
Explanation : Mother’s age is 5 times the age of the daughter.
      Let age of the daughter be x and age of the mother be 5x.
        After 3 years, their ages will be x+3 and 5x+3.
Given that after 3 years, age of mother will be 4 times the age of daughter.
The ratio of the ages of mother and daughter after 3 years = 4:1
            Therefore,
5x+3 / x+3
=
4 / 1
=>5x+3 = 4x+12
                                      =>x=9
  Present age of the daughter is 9 years.
After 3 years, age of the daughter will be  x+3 = 9+3 = 12 years

Aptitude Questions with Explanations – Problems on Ages
15. A teacher is 3 times as old as his student. 5 years hence, teacher will be 2 ½ times as old as his student. What is the difference between the ages of teacher and student?
a)40 years    b)50 years      c)60 years     d)5 years
Answer :
Explanation:  Let the age of the student be x years . Teacher’s age = 3x
             After 5 years, their ages will be x+5 and 3x+ 5.
After 5 years, their ages will be in ration: 1: 2 ½ =2:5
             
x+5 / 3x+5
=
2 / 5
=>5 (x+5)= 2(3x+5) =>5x+25=x+10 =>x=15 years.
       The difference between their ages is=>3x-x=2x =2 x 15 = 30 years

Problems on Ages solved problems for Competitive Exams
16.  6 years ago, the ratio of ages of A and B was 5:6 and 4 years hence, the ratio of their ages will be 10:11. What is the present age of B?
a) 10 years    b) 12 years      c)15 years       d)16 years
Answer:
Explanation:
6 years ago, the ages of A and B were in the ratio of 5:6.
6 years ago, let the age of A and B were 5x and 6x .
Their present ages = 5x+6 and 6x+6
After 4 years , their ages will be in the ratio 10:11
After 4 years , age of A and B will be 5x+6+4  and  6x+ 6 +4 => 5x+10 and 6x+10
5x+10 / 6x+10
=
10 / 11
=>55x+110 = 60x+100 => x=2.
Present age of B= 5x+6 = 5 x 2 +6 =16 years

 Aptitude for Campus Placements : Problems on Ages solved questions 17.
17. The sum of the ages of a father and son is 50 years. 5 years ago, the age of the father was 7 times the age of the son. What will be age of the father after 7 years?
a)42 years     b)35 years    c)45 years       d)49 years
Answer: D
Explanation: 5 years ago, the age of the father was 7 times the age of the son.
   5 years ago , the age of the son was x and father was 7x.
Present sum of the ages of father and son = 50 years
5 years ago, their sum of the ages was 50 – 2x5 = 40 years
               Age of the father , 5 years ago= 40 x
7 / 8
  =35 years
   Present age of the father= 35+5 = 40 years
After 9 years, age of the father will be = 40 +7 = 47 years.

GMAT Quantitative Aptitude study material – Problems on Ages
18. The ratio of the ages of A and B is 1:4 and the product of their ages is 256. What will be the ratio of their ages after 8 years?
a) 3:5    b)10:3        c)3:10   d)None of these
Answer :C
Explanation:  let the age of A and B be x and 4x.
   Product of their ages = x x 4x =4x2 =256 =>x=8
   Present age of A and B = x and 4x = 8 years and 32  years
             Ratio of their ages after 8 years will be = 8+8 : 32+8
=16:40= 2:5

Arithmetic free study material- Age related Problems
19. At the time of marriage Siva was 6 years elder to his wife and 12 years after the  marriage  his age was
6 / 5
times the age of his wife. What was the age of his wife at the time of marriage?
a) 20 years    b)24 years     c)28 years     d)32 years
Answer : B
Explanation : Let the age of Siva at the time of marriage be x years.
              Then, age of Siva’s wife at the time of marriage = x-6 years
            After 12 years , ratio of their ages was 6:5.
The difference between their ages = 6-5= 1 part = 6 years
Their ages 12 years after their marriage were 6x6 and 5x6 = 36 and 30.
           At the time of marriage, their ages were, 36-12 and 30-12 = 24 and 18
  Therefore, at the time of marriage, age of Siva's wife was =18 years

Aptitude Questions with Explanations – Problems on Ages
20. After 15 years the age of Murthy will be 4 times the age which was 15 years ago. Find the present age of Murthy?
a) 25 years    b)30 years     c)35 years     d)40 years
Answer: A
Explanation:  Let the present age of Murthy be x years.
       15 years ago, his age was= x-15.
        After 15 years, his age will be = x+15
After 15 years , he will be 5 times the age which was 20 years ago
         =>(x+15) =4(x-15)
         => 4x-60= x+15 =>x= 25 years
Alternate method:
        The ratio of the ages of Murthy 15 years ago and 15 years hence= 4:1
         The difference between these two = 15 +15 = 30 years
                4-1 = 3 parts = 30 years =>1 part=10
     Age of Murthy after 15 years = 4x 10 = 40 years

             Therefore, present age of Murthy = 40-15 = 25 years.