Aptitude Discussion

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 |

**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.**

**Shubham Gupta**

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**Sravan Reddy**

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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**

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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 $y=4$.

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?