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

**Problem**

**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* = 2*A* i.e.

And *B* = 3*C* 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 1000^{th} of the capital invested by A, B and C respectively.

Now, 2*a* = *b* and *b* = 3*c*

i.e. 2*a* = 3*c*

Thus 2*a* 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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