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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 56

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

Ratio Proportion

Problem

Three types of tea each worth $6.00 / lb, $7.50 / lb and $x / lb are mixed in proportion of 1 : 2 : 3 to form a mixture worth $8.50 / lb. What is the value of x in $ / lb?

  1. 7.00
  2. 7.50
  3. 8.00
  4. 8.50
  5. 10.00

The Usual Method

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Let the quantities of each type of $6.00, $7.50 and $x of tea be 1 lb, 2 lbs and 3 lbs respectively as per their proportions.

Hence total worth of tea = 6\times 1+7.5\times 2+x\times 3

=6+15+3x

=21+3x

Hence cost / lb = \frac{21+3x}{6}

This is equal to $8.50 / lb

\therefore \frac{21+3x}{6}=8.50

\therefore 21+3x=8.5\times 6=51

\therefore 3x=30

\therefore x=10

(Ans: 5)

Estimated Time to arrive at the answer = 60 seconds.

Using Technique

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Observe that if two types of tea of $6 and $7.50 to be mixed with a third type of $x to form a mixture costing $8.50, the cost of the third type of tea should be more than $8.50. This means that you can eliminate all other options except ‘5’ i.e. $10 which is the answer.

(Ans: 5)

Estimated Time to arrive at the answer = 5 seconds.
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