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# [Smart Math] Ratio Proportion Problem 26

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 ${}^{1}\!\!\diagup\!\!{}_{10}\;$th of the total capital. What is A’s capital? 1.$3000
2. $3100 3.$3250
4. $3300 5.$6000

### The Usual Method

Let the capital of A be A, B be B and C be C.

Hence, B = 2A i.e. $\frac{A}{B}=\frac{1}{2}$

And B = 3C i.e. $\frac{B}{C}=\frac{3}{1}$

Hence,   A      :           B         :           C

=          1          :           2

3          :           1

=          3          :           6          :           2

Capital invested = 1100 x 10 = 11000

Hence A’s capital = A = $\frac{11000}{\left( 3+6+2 \right)}\times 3=3000$

(Ans: 1)

Estimated Time to arrive at the answer = 45 seconds.

### Using Technique

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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