Here’s and example of a **SMART MATH** problem for **TIME SPEED DISTANCE.**

**Problem**

**Problem**

A monkey climbs 30 meters of a pole during the day and slips down by 10 meters at night. Assuming that days and nights are equal, in how many days will the monkey scale a 120 meters high pole?

**The Usual Method**

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During the course of the whole day and whole night the monkey will climb 30 – 10 = 20 meters.

To scale 120 meters pole, the monkey would take days.

However, on the end of the 6^{th} day, the monkey would have actually climbed 120 + 10 = 130 meters.

We can form a table where the day number and night number are given with the position of the monkey at the end of that period (day / night).

Day # aaa Position aaaaaaaa Night # aaaaaaaaaa Position

1 30 1 20

2 50 2 40

3 70 3 60

4 90 4 80

5 110 5 100

6 130 6 120

As can be seen from the table, that at the end of 5^{th} day the monkey climbs 110 meters and thereafter slips in the night by 10 meters, to reach 100 meters. Now to reach 120 meters during the 6^{th} day, the monkey needs of the 6^{th} day. Since the complete day has equal duration of both day time and night time, the 2/3 of day time is equivalent to 1/3 of the whole day (Day time and night time together). Hence total duration needed to reach 120 meters = days.

**(Ans: 1)**

*Estimated Time to arrive at the answer = 100 seconds.*

**Using Technique**

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During the course of a complete day, the monkey climbs 30 – 10 = 20 meters, so to climb 120 meters, it will take days. We know that since the monkey has slipped during the 6^{th} night, the total complete days needed to reach 120 meters has to be less than 6 days. This eliminates all options from ‘3’ to ‘5’. This means that the answer can be or days. You can simply check that in 5 complete days, the monkey climbs 5 x 20 = 100 meters. Since during day time, the monkey climbs 30 meters, so to climb the balance (120 – 100) 20 meters, of the 6^{th} day time will be used. Since the complete day has equal duration of both day time and night time, the 2/3 of day time is equivalent to 1/3 of the whole day (Day time and night time together). Hence total duration needed to reach 120 meters = days.

(Note: Students commit mistakes in considering day time as whole day and get the answer as days in stead of days).

**(Ans: 1)**

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

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