The Spotting Contest

During a recent plane and train spotting contest, five eager entrants were lined up ready to be tested on their spotting ability. 

They had each spotted a number of planes (26, 86, 123, 174, 250) and a number of trains (5, 42, 45, 98, 105). From the clues below, can you determine what colour shirt each was wearing, their position, their age (21, 23, 31, 36, 40) and the number of trains and planes spotted?

1. Bob spotted 44 less trains than planes. 

2. Tom was 36 years old. 

3. The person on the far right was 8 years younger than Bob, and spotted 174 planes. 

4. Josh was wearing a yellow shirt and spotted 37 trains fewer than Bob. 

5. The person who was wearing a green shirt, was 19 years younger than the person to his left. 

6. Steven spotted 105 trains and 250 planes.

7. The person in the center was 31 years old, was wearing a blue shirt and spotted 42 trains.

8. Doug, who was on the far left, spotted 26 planes, and spotted 72 trains more than planes. 

9. The person who was wearing a red shirt was 4 years older than Tom and was not next to the person wearing a blue shirt. 

10.The person who was next to the 31 year old, but not next to the person who spotted 26 planes, was wearing a orange shirt, and spotted 45 trains. 

Here are final STATS of the contest! 

Final Stats of The Spotting Contest

What was the contest?

Five participants having ages (21, 23, 31, 36, 40) had each spotted a number of planes (26, 86, 123, 174, 250) and a number of trains (5, 42, 45, 98, 105). 

Below are the clues given - 


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1. Bob spotted 44 less trains than planes. 

2. Tom was 36 years old. 

3. The person on the far right was 8 years younger than Bob, and spotted 174 planes. 

4. Josh was wearing a yellow shirt and spotted 37 trains fewer than Bob. 

5. The person who was wearing a green shirt, was 19 years younger than the person to his left. 

6. Steven spotted 105 trains and 250 planes. 

7. The person in the center was 31 years old, was wearing a blue shirt and spotted 42 trains. 

8. Doug, who was on the far left, spotted 26 planes, and spotted 72 trains more than planes. 

9. The person who was wearing a red shirt was 4 years older than Tom and was not next to the person wearing a blue shirt. 

10. The person who was next to the 31 year old, but not next to the person who spotted 26 planes, was wearing a orange shirt, and spotted 45 trains. 

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STEPS : 

Let's make at table like below and fill the data one by one.

 
STEP 1 : 

As per (3), the person on the far right that is at position 5 had spotted 174 planes & he must be 23 years old so that Bob aged 31 years (only pair of ages having 8 years difference.

 
STEP 2 : 

As per (7), the person at position 3 who is wearing blue shirt and is 31 year old. He has spotted 42 trains.

STEP 3 : 

For (5) to be true, the ages of those participants occupying consecutive positions must be 40 and 21 respectively. Only, positions lefts for (5) to be true are 1 & 2.

STEP 4 : 

And as per (8), the person at position 1 must be Dough who spotted 26 planes and spotted 72  trains more than planes i.e. 26 + 72 = 98 trains.

STEP 5 : 

As per (10), the person at position 4 must be wearing orange shirt and must have spotted 45 trains. His age must be 36 years (only number in ages list left).

STEP 6 :

As per (9) suggests, Tom must be 36 years old positioned at 4 and Dough must be the person wearing red shirt. With that, Josh in (4) must be wearing yellow shirt and positioned at no.5. 

STEP 7 : 

The hint (4), also suggests that Josh must had spotted 5 trains out of 42-5 possible spotted trains pair shared with Bob. Hence, the person at 2nd position must had spotted 105 trains (only number left in list of number of trains spotted).
 

STEP 8 : 

As per (3), the person having age 31 must be Bob. Hence, at no.2, Steven must be there. 

STEP 9 : 

As per (6), Steven have spotted 250 planes. As per (1), Bob must have spotted 42 + 44 = 86 planes. And the only number left as number of planes spotted for Tom is 123.

STEP 10 :

Final Stats look like as - 

Count The Number of Kids

Fourteen of the kids in the class are girls. Eight of the kids wear blue shirts. Two of the kids are neither girls or wear a blue shirt. If five of the kids are girls who wear blue shirts, how many kids are in the class?

Find The Count Here!
 

Count of Number of Kids.

 Read the problem first!

 Let's recollect all the data given in the question.

1.Fourteen of the kids in the class are girls.

2. Eight of the kids wear blue shirts. 

3.Two of the kids are neither girls or wear a blue shirt.

4.Five of the kids are girls who wear blue shirts.

Now, (3) clearly suggests that there are 2 boys who are not wearing blue shirts. 

From (5) and (2), it's clear that 3 of 8 kids who are wearing blue shirts are boys as 5 of them are girls.

Above 2 conclusions indicates that there are total 5 boys in the class; 2 not wearing blue shirts and 3 wearing blue shirts.

But as per (1), there are 14 girls in a class. 

Hence, total 14 + 5 = 19 kids are there in a class.