Algebra
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Q.

The total age of some 7 years old and some 5 years old children is 60 years. If I have to select a team from these children such that their total age is 48 years, In how many ways can it be done?

 A.

3

 B.

2

 C.

1

 D.

4

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Solution:
Option(C) is correct

Let $a$ children of 7 years and $b$ children of 5 years be taken. 

Then, $7a+5b=48$

This is possible only when $x=4$ and $b=4$

Hence, only one combination is possible.

Edit: For an alternative explanation, check comment by Lemini.

Edit 2: For yet another alternative solution, check comment by Sravan Reddy.


(3) Comment(s)


Shubham Gupta
 ()

The language of the question isn't very clear.

My interpretation of the question was that from given initial condition (total age of some 7-year olds + some 5-year olds = 60), we can infer that there are 5 7-year olds (total age 35) and 5 5-year olds (total age 25). In this way, total age = 25 + 35 = 60.

Now for having a team of sum-of-age as 48, we need 4 7-year olds (total age = 28) and 4 5-year olds (total age = 20). For this no of ways of selection would be (5C4)x(5C4) = 25.

But alas! 25 is not even an option.

Is this interpretation of the given question and the subsequent solution correct? I mean, if we don't look at the 4-options for a while, is it a correct way to interpret and solve this question?



Sravan Reddy
 ()

Some thinking process to get to combinations quickly: (may seem lengthy but it takes less than 20 sec while doing it in mind)

How many 7's and how many 5's make 60. As 5 multiples can only end with 5 or 0, the 7 multiple should end with 0 or 5 for the sum to be possible. So, either 0 or 35 is the option. So, it can be '0' 7 year children and '12' 5 year children or '5' 7 year children and '5' 5 year children

How many 7's and 5's make 48 now?

we need to remove a multiple of 7 which ends with '8' or '3' so that the remaining part will be a multiple of 5. So, possible multiples of 7 are 28 and 63. Only 28 is possible.

So, 28 (7*4) and 20 (5*4) - '4' 7 year children and '4' 5 year children



Lemini
 ()

I think the question can be explained in a better manner. Here is my take on the question:

The total sum of the age given is 60,which can come from only one combination,which is $x=5$ and $y=5$ where $x$ and $y$ is children of 7 years and 5 years respectively.So we have 10 children in total.

In similar manner to get the total sum of ages to be 48,the number of 7 year children should be 4 and 5 year children should be 4.

So the answer is $x=4$ and $y=4$.