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problems on ages
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Exercise 2
Exercise 1
1.
Jayant is as much younger to Arun as he is older to Prashant. If the sum of the ages of Arun and Prashant is 48 years,what is the age of Jayant?
A.
21 years
B.
22 years
C.
23 years
D.
24 years
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Answer:
D
Explanation :
Let Arun's age = x years
then prashant's age = (48- x) years.
Now, let the age of jayant is y years
Then, by question,
(x-p) = p - (48-x) = P = 24.
2.
The ratio between Ram and Mohan ages two years ago was 3 : 2 and at present it is 7 : 5. Find their present ages.
A.
14 years, 10 years
B.
15 years, 20 years
C.
13 years, 9 years
D.
10 years, 25 years
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Answer:
A
Explanation :
At present,
Let x: y = 7 : 5
and 2 years back, p : q = 3 : 2
and
T = 2 years
then, by direct formula
At present, Ram's age = ˣX[(p-q)T / xq-yp]
= 7X [(3-2)X2 / 14-15]
= 7 X 2 = 14 years
Similary, mohan's age = y X 2
= 5 x 2 = 10 years
3.
Aruna got married 6 years ago. Today her age is 14 times her age at the time of marriage. Her Son age is (1/10) times her age. Her Son age is
A.
1 years
B.
2 years
C.
3 years
D.
4 years
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Answer:
C
Explanation :
6 years ago, let Aruna's age = x years.
Then Aruna's present age = (x + 6) years
Therefore by question,
x + 6 = 5/4 X ˣ
(x + 6) X 4 = 5x
x = 24
Therefore Aruna's present age = 24 + 6 = 30 years.
Therefore son's present age = 1/10 X 30 = 3 years
4.
In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, find the present age of B?
A.
39 years
B.
40 years
C.
41 years
D.
38 years
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Answer:
A
Explanation :
Let the present age of B = x years.
then, A's age is (x + 9) years.
Therefore by question.
(x + 9 + 10) = 2 (x- 10)
or, x + 19 = 2 X- 20
or,
x = 39 years
Hence, B' s age is 39 years at present.
5.
The ratio of the ages of A and B is 3:11. After 3 years the ratio becomes 1:3. What are the ages of A and B?
A.
9 years, 33 years
B.
10 years, 40 years
C.
9 years, 18 years
D.
8 years, 35 years
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Answer:
A
Explanation :
Let
x: y = 3
:11 and
T = 3 years
p:q = 1 :3
Now applying direct formula,
A's age = ˣX[(p-q)T / xq-yp]
= 3 x 1[(1-3)x3 / 9-11] = 3 x 3 = 9 years
Hence, B's age yX [(p-q)T / xq-yp]
= 11 x 3 = 33 years.
6.
The ratio of the ages of Mohan and Meera is 3 : 4. Four years earlier the ratio was 5:7. Find the present ages of Mohan and Meera.
A.
24 years, 32 years
B.
30 years, 20 years
C.
32 years, 24 years
D.
25 years, 18 years
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Answer:
A
Explanation :
Let x : y = 3:4
and p : q = 5:7
T = 4
Then, by direct formula
Mohan's age = ˣ X[(p-q)T / xq-yp]
= 3X [(5-7)X4 / 21-20] = 3X [-2X4/1]
= 3X 8 = 24 years
Meera's age = yX [(p-q)T / xq-yp] = 4 X 8 = 32 years
7.
The ratio of present ages of two brothers is 1 : 2 and 5 years back the ratio was 1 : 3. What will be the ratio of their ages after 5 years?
A.
1:4
B.
2:3
C.
3:5
D.
5:6
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Answer:
C
Explanation :
Let the present ages of two brothers be x and 2x years
Then, by question
= x-5 / 2x-5 = 1/3
= 3x-15= 2x - 5
x = 10
Hence their present ages are 10 and 20 years. Now after 5 years, their required ratio
= 10 + 5 / 20 +5 = 15/25 = 3/5 i.e., 3:5
8.
Harsha is 40 years old and Rith is 60 years old. How many years ago was the ratio of their ages 3 : 5?
A.
10 years
B.
20 years
C.
37 years
D.
5 years
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Answer:
A
Explanation :
Let x years ago the ratio of their ages was 3 : 5. by question
40-x / 60-x = 3/5
200 - 5x = 180 - 3x =
2x = 20
Therefore x = 10 years.
9.
Six years back Seema was half that of Rupa in age. Four years hence, the respective ratio of their ages would be 3:5. The present age of Rupa is:
A.
46 yr
B.
40 yr
C.
32 yr
D.
16 yr
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Answer:
A
Explanation :
Let the present ages of Seema and Rupa be x and y.
Six years back,
Seema's age= x -6
Rupa's age = y -6
= (x-6) = 1/2 (y-6)
or 2x-y =6
.......(i)
Four years hence, Seema's age= x + 4
Rupa's age = y + 4
x+4 / y+4 = 3/5
5x+20=3y+12
5x-3y= 8
.........(ii)
Multiply Eq. (i) by 3,
6x-3y=18 .......(iii)
Subtract Eq. (iii) from Eq. (ii),
X =26
Substitute this value of x in Eq. (i),
y=2x-6=2 X 26 -6=52-6=46yr
10.
The ratio of present ages of Raghav and Amit is 7 : 8. If 4 yr ago the ratio of their ages be 5 : 6, then present age of Amit is:
A.
10 yr
B.
12 yr
C.
14 yr
D.
16 yr
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Answer:
D
Explanation :
Let present ages of Raghav and Amit be 7x and 8x.
4 yr ago, Raghav's age = 7x - 4
Amit's age= 8x- 4
Therefore 7x-4 / 8x-4 = 5/6
6(7x- 4) = 5(8x- 4)
42x -24 = 40x -20
2x = 4
X =2
Therefore, Amit's present age= 8 x 2 = 16 yr
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