Here’s and example of a SMART MATH problem for RATIO PROPORTION.
Problem
A, B and C invest in a business with B’s capital being twice that of A’s and thrice C’s. In particular years the profit amounts to $1100, which is th of the total capital. What is A’s capital?
- $3000
- $3100
- $3250
- $3300
- $6000
The Usual Method
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Let the capital of A be A, B be B and C be C.
Hence, B = 2A i.e.
And B = 3C i.e.
Hence, A : B : C
= 1 : 2
3 : 1
= 3 : 6 : 2
Capital invested = 1100 x 10 = 11000
Hence A’s capital = A =
(Ans: 1)
Estimated Time to arrive at the answer = 45 seconds.
Using Technique
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Total investment = 1100 x 10 = 11000 = 11 x 1000
Let a, b and c be 1000th of the capital invested by A, B and C respectively.
Now, 2a = b and b = 3c
i.e. 2a = 3c
Thus 2a should be a multiple of 3, but since, 2 is not a multiple of 3, ‘1’ should be the multiple of 3. The only value that ‘1’ can take from amongst the options is 3 and 6 (or 3000 and 6000).
A’s capital cannot be $6000, as B’s capital will be 2 x 6000 = 12000, which is more than the total capital of $11000, so the answer has to be $3000 or option ‘1’.
(Ans: 1)
Estimated Time to arrive at the answer = 10 seconds.
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