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# [Smart Math] Averages Problem 4

Hereâ€™s and example of a SMART MATH problem for AVERAGES.

### Problem

In a class of 40, there are 10 boys at the age of 12 years, 12 at the age of 12.5 and the rest at the age of 13. The average age of all boys in the class is ___________ years.

1. 12.1
2. 12.2
3. 12.5
4. 12.6
5. 12.7

### The Usual Method

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Total age of 10 boys = 10 x 12 = 120 years

Total age of 12 boys = 12 x 12.5 = 150 years

Total age of the remaining18 boys = 18 x 13 = 234 years

Hence, total age of all students in the class = 120 + 150 + 234 = 504 years

Hence, average age of the class = $\frac{504}{40}=12.6$years.

(Ans: 4)

Estimated Time to arrive at the answer = 60 seconds.

### Using Technique

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Last digit of total age of 10 boys = 0

Last digit of total age of 12 boys = 0 (Note: 12.5 x 12 is same as 25 x 6 and its last digit is 5 x 6 => 0)

Last digit of total age of 18 boys = 4

Hence, last digit of the sum of age of the class = 0 + 0 + 4 = 4.

Also, since there are more students with age of 13 than with the age of 12 or 12.5, the average should definitely be more than 12.5. From the options, we can eliminate all but options â€˜4â€™ and â€˜5â€™.

To choose between options â€˜4â€™ and â€˜5â€™, simply check the last digits of as follows:

For option â€˜4â€™ =>12.6 x 40 = 126 x 4, last digit = 4

For option â€˜5â€™ => 12.7 x 40 = 127 x 4, last digit = 8.

Since only option â€˜4â€™ satisfies the condition of last digit = 4, option â€˜4â€™ is the answer.

(Ans: 4)

Estimated Time to arrive at the answer =15 seconds.

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## 4 replies on “[Smart Math] Averages Problem 4”

vivek garwaresays:

a train going with the speed of 40 km/hr reach on its destination in destined time. It reaches 15 mins late when it travels with the speed of 35 km/hr. Then what will be the total distance it has to travel?

LazyMaths.comsays:

The distance is 70 Kms one way.
The way you can quickly solve this is as follows:
The LCM of 40 and 35 is 280.
So to travel 280 Kms @ 40 Kms/hr, it will take 70 hours and to travel the same distance of 280 Kms @ 35 Kms/hr, it will take 8 hours.
The difference is 1 hour or 60 minutes.
So for a difference of 15 minutes or 1/4th of an hour, simeply do 1/4th of 280 kms which is 280/4 = 70kms.
Thanks

in my sol.. it is 12.5555

LazyMaths.comsays:

Hi Kristian,

12.555… rounded to the tenth digit is 12.6, hence the answer is 12.6.
Thanks