Nine years ago A's age and B's age were in the ratio 5:7 .Which of the following cannot be the ratio of their ages 5 years from now?
Answers
Given : Nine years ago A's age and B's age were in the ratio 5:7
To Find : Which of the following cannot be the ratio of their ages 5 years from now
a) 11/13 b)13:19 c)21.25 d)15:16
Solution:
Nine years ago A's age and B's age were in the ratio 5:7
A = 5K
B = 7K
Present ages = 5K + 9 and 7K + 9
ages 5 years from now = 5K + 9 + 5 , 7K + 9 + 5
= 5K + 14 and 7K + 14
ratio of their ages 5 years from now
= (5K + 14)/(7K + 14)
(5K + 14)/(7K + 14)
= (5K + 10)/(7K + 14) + 4/(7K + 14)
= 5(K + 2)/7(K + 2) + 4/(7K + 14)
= 5/7 + 4/(7K + 14)
Hence (5K + 14)/(7K + 14) > 5/7
Hence ratio of their ages 5 years from now > 5/7
Options are
a) 11/13 b)13:19 c)21.25 d)15:16
Lets check one by one
11/13 > 5/7
=> 77 > 65
TRUE , Hence possible
13/19 > 5/7
=> 91 > 95
Not true Hence not possible
21/25 > 5/7
=> 147 > 125
True , Hence possible
15/16 > 5/7
=>105 > 80
True , Hence possible
Hence 13: 19 can not be the ratio of their ages 5 years from now
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