Categories
Ratio Proportion Smart Math

[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 2/3rd 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

[contentblock id=google-adsense-post]

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.
[starrater tpl=10]

[contentblock id=smartmath-blockquote]

Leave a Reply

Your email address will not be published.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