Categories
Averages Smart Math

[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?

  1. 60
  2. 62
  3. 64
  4. 66
  5. 68

The Usual Method

[contentblock id=google-adsense-post]

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

[contentblock id=google-adsense-post]

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=60lbs

(Ans: 1)

Estimated Time to arrive at the answer = 15 seconds.
[starrater tpl=10]

[contentblock id=smartmath-blockquote]

Leave a Reply

Your email address will not be published. Required fields are marked *