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# [Smart Math] Ratio Proportion Problem 40

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

### Problem

$6200 is divided between P, Q, R and S such that Q’s share is 2/3rd of P’s and R’s is 5/6th of Q’s and S’s share is equal to that of Q and R together. What is P’s share? 1.$900
2. $2500 3.$2200
4. $1800 5.$2000

### The Usual Method

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

$\therefore P:Q=3:2$

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

$\therefore Q:R=6:5$

$S=R+Q$

$\therefore$      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 [contentblock id=google-adsense-post] 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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