[Smart Math] Ratio Proportion Problem 40

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

Ratio Proportion

Problem

$6200 is divided between P, Q, R and S such that Q’s share is 2/3^rd of P’s and R’s is 5/6^th of Q’s and S’s share is equal to that of Q and R together. What is P’s share?

$900
$2500
$2200
$1800
$2000

The Usual Method

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$Q=\frac{2}{3}P$

$\therefore P:Q=3:2$

$R=\frac{5}{6}Q$

$\therefore Q:R=6:5$

$S=R+Q$

$\therefore$ P : Q : R

3 : 2

6 : 5

9 : 6 : 5

$\therefore$ S = 6 + 5 = 11

$\therefore$ P : Q : R : S = 9 : 6 : 5 : 11

Hence share of P = $\frac{9}{9+6+5+11}\times 6200=\frac{9}{31}\times 6200$ = $1800

(Ans: 4)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

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Note that $Q=\frac{2}{3}P$

$\therefore P:Q=3:2$

$\therefore$ P = 3x and Q = 2x

Hence P’s share = multiple of 3. Only options ‘1’ and ‘4’ are multiples of 3. Thus all other options are eliminated.

Also note from the statement of the question itself that P > Q > R and S being Q + R, may be equal to, or less than or greater than P. Thus P’s share is significant.

$900 out of $6200 is not so significant as $1800 out of $6200. Hence $1800 is the share of P.

(Ans: 4)

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

The Usual Method

Using Technique

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