Problems On Ages
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7 years ago, the ages (in years) of A and B were in the ratio 4 : 5; and 7 years hence they will be in the ratio 5 : 6. The present age of B is
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56 years
-
63 years
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70 years
-
77 years
D.
77 years
After 7 years, Required age
= 5x + 7 = 5 x 14 + 7 = 77 years
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In one hour, a boat goes 12 km along the stream and 8km against the stream. The speed of the boat in still water is
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12 km/h
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11 km/h
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10 km/h
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8 km/h
C.
10 km/h
Speed of boat = 
= 
The present ages of A and B are in the ratio 3 : 4. Ten years ago, this ratio was 4 : 7. The present age of A and B are respectively:
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18 years, 24 years
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21 years, 28 years
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24 years, 32 years
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27 years, 36 years
A.
18 years, 24 years
Let present age of A = 3x
And present age of B = 4x
According to the question,
∴ Present age of A = 3x = 3 x 6 = 18 years
Present age of B = 4x = 4 x 6 = 24 years
The sum of the age of mother and a mother and her daughter is 60 years. 12 years ago the mother was eight times as old as her daughter. How old is the daughter at present?
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20 yr
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28 yr
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16 yr
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12 yr
C.
16 yr
Let, present age of mother = M Years
and present age of daughter = D Years.
Now, according to the question,
M + D = 60 ...(i)
and (M − 12) = 8(D−12) 
M−12 = 8D−96
M − 8D = −84
Now, solving Eqs. (i) and (ii), we have
D = 16 years
Hence, the present age of daughter = 16 years.
The sum of the ages of two brothers, having a difference of 8yr between them, will double after 10 yr. What is the ratio of the age of the younger brother to that of the elder brother?
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7 : 11
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3 : 7
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8 : 9
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10 : 13
B.
3 : 7
Let the present age of two brother's be x yr and (x + 8) yr.
After 10 yr,
Ages of two brothers (x + 10)
and (x + 8 + 10)
According to the question,
x + 10 + x + 18 = (x + x + 8) x 2
2x + 28 = (2x + 8) x 2
2(x + 14) = (2x + 8) x 2
x + 14 = 2x + 8
x - 2x = 8 - 14
-x = -6 or x = 6
Required ratio = 
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