CBSE Class 8 Answered
2) A motor boat covers a certain distance downstream in a river in five hours. It covers the same distance upstream in five hours and a half. The speed of the water is 1.5km/hr. What is the speed of the boat?
3) A man is 5 years older than his wife and the wife is now thrice as old as their daughter, who is 10 years old. How old was the man when his daughter was born?
4) Two years ago, Dilip was three times as old as his son and two years hence, twicw his age will be equal to five times that of his son. what is the present age of Dilip?
Expert Answer
1) Let digit at the tens place = x years
Let digit at the units place =y years
Then the number formed is represented by 10x + y.
Also if the digits are reversed, the number formed is 10y + x.
According to the given conditions, age of man is same as his wife's age but the digits are reversed.
Age of man = 10x + y
Age of wife = 10y + x
By conditions, sum of their ages is 99.
10x + y + 10y + x = 99
11x + 11y = 99
x + y = 99 ...... (i)
Also given is the man is 9 years older than his wife.
10x + y = 10y + x + 9
10x + y - 10y - x = 9
9x - 9y = 9
x - y = 1 .....(ii)
Solving equations (i) and (ii) we get,
x = 5 and y = 4
Hence the age of man is 54 years and age of wife is 45 years.
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Topperlearning Team.
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