## 4 Moderate Problems From Weights & Ages

Below are given 4 problems from ages and weights.

Question 1

In Charan's opinion, his weight is not more than 24 kg. His friend thinks that Charan's weight is greater than 20 kg but lesser than 25 kg. His mother's view is that his weight cannot be less than 22 kg. If all of them are correct in their estimation, what is the average of different probable weights of Charan?

Solution:

Let the weight of Charan be x
in his view, x < = 24 ...(1)
in his friend's view, 20 < x < 25 ...(2)
in his mother's view, x > = 22 ...(3)

Combining (1),(2) and (3) we have 20 < 22 < = x < 24 < 25
Simplifying, we get : 22 < = x < = 24
Therefore, the probable weights are 22,23 and 24.
Average of probable weights = (22+23+24)/3 = 69/3 = 23.

Question 2

Arun says that his weight is in the range of 58 kg to 64 kg. His brother weight is 62 kg and Arun's weight is not more than that of his brother's. Also, as a matter of fact, Arun's weight is in between 60 kg and 65 kg. If all the above statements are true, then find the average weight of Arun.

Solution:

Let the weight of Arun be x.
In Arun's view, 58 < x < 64 ...(1)
Based on his brother's estimation we have x < = 62 ...(2)
also given that 60 < x < 65 ...(3)
Combining, (1),(2) and (3) we have 58 < 60 < x < = 62 < 64 < 65
Simplifying the above inequality, we get, 58 < x < = 62
Probable values for x are 59,60,61 and 62
Average of the probables are(59+60+61+62)/4 = 242/4 = 60.5

Question 3

The average age of husband, wife and their child 4 years ago was 32 years and that of wife and the child 3 years ago was 25 years. The present age of the husband is:
a) 53 years b)52 years c)50 years d)None of these

Solution :

Let the present age of husband, wife and child be x, y, z respectively
Given that 4 yrs ago the average is 32
i.e. [(x-4)+(y-4)+(z-4)]/3 = 32
we have x+y+z= 108 ----(1)
Also given that 3 years ago the average is 25
i.e. [(y-3)+(z-3)]/2 = 25
we have y+z = 56 ------(2)

Substituting y + z = 56 in eq 1 we get,
x + 56 = 108
Or x = 52

Question 4

Before 5 years, the sum of the ages of Ragu and Suresh was 80 years. The sum will be 104 years after 7 years. What could be possible combinations of ages from among the options.

a) 50,40 b) 25,65 c) none of these d)both a & b

Answer : d) both a & b

Solution:

Let the age of Ragu be x and that of Suresh be y

Before 5 years, the sum of ages was 80, i.e x - 5 + y - 5 = 80
Or x + y = 90 ...(1)

After 7 years, the sum will be 104, i.e x + 7 + y + 7 = 104
Or

i.e. x + y = 90 ...(2)

Equations 1 and 2 indicate that the sum of the ages has to be 90.

Both option a and option b have listed ages whose sum is 90. Hence there are two possible solutions from among options. Hence option d) is correct answer.

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