[Smart Math] Averages Problem 10

Here’s and example of a SMART MATH problem for AVERAGES.

Averages

Problem

The average weight of a sac of wheat in a truck is reduced by 0.2 lbs from 50 lbs when 5 new sacs, each weighing 47.4 lbs on an average, are loaded. How many sacs did the truck originally carried?

The Usual Method

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Let there be ‘x’ number of sacs in the truck originally.

Hence total weight of the load in the truck = 50x

New number of sacs = x + 5

New average weight = $(x+5)\times 49.8$ = (49.8x + 249) lbs

Total weight of new sacs = 47.4 x 5 = 237 lbs

Hence 49.8x + 249 = 50x + 237

$\therefore 0.2x=12$

$\therefore x=\frac{12}{0.2}=60$

(Ans: 1)

Estimated Time to arrive at the answer = 60 seconds.

Using Technique

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Difference between the average weight of the original sacs and the new sacs = 50 – 47.4 = 2.6lbs

Total difference = 2.6 x 5 = 13 lbs. Now this 13 lbs is reduced from the total weight of (x + 5) bags and the reduction is that of 0.2 lb each. Hence $\frac{13}{x+5}=0.2$

$\therefore x+5=65$

$\therefore x=60$ lbs

(Ans: 1)

Estimated Time to arrive at the answer = 15 seconds.
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Problem

The Usual Method

Using Technique

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