Here’s and example of a SMART MATH problem for RATIO PROPORTION.
Problem
The ratio of number of ladies to gents in a party was 3 : 2. When however, 20 more gentlemen joined the party, the ratio was reversed. How many ladies were there at the party?
- 16
- 24
- 32
- 36
- 40
The Usual Method
[contentblock id=google-adsense-post]
Let ‘x’ be the constant of proportionality. Hence, there will be 3x ladies and 2x gents in the party originally.
New total number of gents = 2x + 20
Hence, ratio of ladies to gents =
Original number of ladies = 3x = 3 x 8 = 24
(Ans: 2)
Estimated Time to arrive at the answer = 45 seconds.
Using Technique
[contentblock id=google-adsense-post]
Since the total number of ladies at the party = 3x, the answer should be a multiple of 3. From the options, only option ‘2’ and ‘4’ are multiples of 3. Assuming option ‘2’ to be the right answer, the number of men becomes 2x = 16 (using 3x = 24 ) Hence, new total of gents = 20 + 16 = 36 and 24 : 36 = 2 : 3. This satisfies the conditions and so, ‘2’ is the right option.
(Ans: 2)
Estimated Time to arrive at the answer = 15 seconds.
[starrater tpl=10]
[contentblock id=smartmath-blockquote]