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

**Problem**

**Problem**

Divide $1000 in two parts, so that if the two parts are invested @ 4% and 5% simple interest, the total yearly income may be $46.50.

- $350 @ 4%; $650 @ 5%
- $650 @ 4%; $350 @ 5%
- $400 @ 4%; $600 @ 5%
- $600 @ 4%; $400 @ 5%
- $500 @ 4%; $500 @ 5%

**The Usual Method**

[contentblock id=google-adsense-post]

Let the investment @ 4% be ‘*x*’.

Hence, investment @ 5% = (1000 – *x*)

Interest earned =

Hence, amount invested @ 4% = $350

And amount invested @ 5% = $650

**(Ans: 1)**

*Estimated Time to arrive at the answer = 60 seconds.*

**Using Technique**

[contentblock id=google-adsense-post]

Should the two parts invested be equal in size i.e. $500 each, the earning will be $45 (average of 40 and 50). But since the actual earning is more than $45 (46.50 > 45.00), the amount invested at 5% is more than the amount invested at 4%. (Using the concept of weighted average, where average tends to shift towards the higher weight). Hence, amount invested @ 4% is less than $500 and that invested @ 5% is more than $500. The only options satisfying this are ‘1’ and ‘3’.

Option ‘3’ is eliminated by working backwards:

Hence, option ‘1’ is the right option.

**(Ans: 1)**

*Estimated Time to arrive at the answer = 15 seconds.*

[starrater tpl=10]

[contentblock id=smartmath-blockquote]