IQ Test Questions With Answers | PDF | Speed | Test (Assessment) - Free Printable

Let’s solve each problem one by one, carefully and step by step.

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Problem 1:
Two people walk in opposite directions. Each walks 6 miles forward, then turns right and walks 8 miles. How far are they from their starting positions?

Think of this as two right triangles — one for each person.

Each person:
- Walks 6 miles straight (let’s say north or south)
- Turns right → now walking east or west
- Walks 8 miles

So each forms a right triangle with legs 6 and 8.

Use Pythagoras:
Distance = √(6² + 8²) = √(36 + 64) = √100 = 10 miles

Since both do the same thing but in opposite directions, each is 10 miles from start.

✔ Answer for Problem 1: 10 miles each

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Problem 2:
A person has some cows and birds. Total eyes = 172, total legs = 344. How many cows and birds?

Let:
- C = number of cows (each has 2 eyes, 4 legs)
- B = number of birds (each has 2 eyes, 2 legs)

Equations:
Eyes: 2C + 2B = 172 → divide by 2 → C + B = 86 ...(1)
Legs: 4C + 2B = 344 ...(2)

Subtract equation (1) multiplied by 2 from equation (2):

From (1): 2C + 2B = 172
Equation (2): 4C + 2B = 344
Subtract: (4C + 2B) - (2C + 2B) = 344 - 172 → 2C = 172 → C = 86

Wait — that can’t be right. If C = 86, then from (1): B = 0? But let’s check legs: 4*86 = 344 → yes, matches. And eyes: 2*86 = 172 → also matches.

But that means there are 86 cows and 0 birds? That seems odd, but mathematically correct.

Wait — maybe I made a mistake in setup?

Actually, if all animals have 2 eyes, then total animals = 172 / 2 = 86.

If all were birds, legs would be 86 * 2 = 172. But we have 344 legs — which is exactly double. So every animal must have 4 legs → all are cows.

Yes! So 86 cows, 0 birds.

✔ Answer for Problem 2: 86 cows, 0 birds

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Problem 3:
Person has socks (red/blue) and shoes (black/brown). Minimum number to take to guarantee at least one matching pair of socks AND one matching pair of shoes?

Worst case scenario:

Socks: You could pick 1 red, 1 blue → no pair yet. Next sock (3rd) will match one → so need 3 socks to guarantee a pair.

Shoes: Similarly, 1 black, 1 brown → no pair. 3rd shoe guarantees a pair.

But wait — you’re taking items blindly. To guarantee BOTH a sock pair AND a shoe pair, you need to consider worst case for both together.

Actually, since socks and shoes are separate categories, you handle them separately.

Minimum to guarantee sock pair: 3
Minimum to guarantee shoe pair: 3
Total: 3 + 3 = 6

Is that safe? Let’s test:

Suppose you take 2 socks (R,B), 2 shoes (Blk,Brn) → no pairs.
Take 3rd sock → now you have a sock pair.
Take 3rd shoe → now you have a shoe pair.
Total taken: 6 items.

Could you get lucky with fewer? Yes, but question asks for minimum to GUARANTEE.

✔ Answer for Problem 3: 6 items

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Problem 4:
Number multiplied by 13 > 105 by same amount it is < 105 less than 105. Find the number.

Let the number be x.

“Multiplied by 13 exceeds 105 by same amount that it falls short of 105” — wait, re-read:

“A number when multiplied by 13, it exceeds greater than 105 by an amount with which it is lower than 105 less than 105.”

This is poorly worded. Let me interpret:

Probably means:
13x - 105 = 105 - x

Because “exceeds 105 by same amount that it is less than 105”

So:

13x - 105 = 105 - x
→ 13x + x = 105 + 105
→ 14x = 210
→ x = 15

Check:
13 * 15 = 195
195 - 105 = 90
105 - 15 = 90 → yes, equal.

✔ Answer for Problem 4: 15

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Problem 5:
When father was celebrating his 50th birthday, son said: “At that time, my age was half of yours.” Now, how old is son?

Wait — “when father was 50”, son said “my age was half of yours” → so at that time, son was 25.

Now, how much time has passed? The problem doesn’t say! It just says “now”.

Wait — reread: “When my father was celebrating his 50th birthday... At that time, I was half your age.” Then it says “How old am I now?”

But we don’t know how many years have passed since then. Unless...

Ah — perhaps the key is: the son is speaking NOW, referring to when father was 50. But if father is still alive and son is talking now, we need more info.

Wait — maybe it’s implying that the father is STILL 50? No, that doesn’t make sense.

Alternative interpretation: Maybe the son is saying that AT THE TIME OF FATHER’S 50TH BIRTHDAY, the son’s age was half of father’s age → so son was 25 then.

But without knowing current year or how many years passed, we can’t find son’s current age.

Unless… perhaps the trick is: the son is speaking on the father’s 50th birthday? But then he’d be 25 now.

The problem says: “When my father was celebrating his 50th birthday...” — past tense. Then “how old am I now?” — present.

But no time gap given. This might be a trick question.

Wait — another thought: maybe “now” refers to the time of the statement, which is during the celebration? But it says “was celebrating”.

Perhaps it’s a language issue. In many such puzzles, it’s implied that the event happened recently or the ages are being compared at that moment.

But logically, if at father’s 50th, son was 25, and if we assume that “now” is that same day, then son is 25.

Maybe that’s the intended answer.

Alternatively, perhaps the son is older now, but we have no data.

I think the only logical assumption is that the son is speaking at the time of the celebration, so “now” = when father is 50, son is 25.

✔ Answer for Problem 5: 25 years old

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Problem 6:
My successor’s father is my father’s son, and I don’t have any brothers or sons. Who is my successor?

Let’s break it down.

“I don’t have any brothers or sons.” → So I am male (since I have a father’s son who is not my brother — must be me).

“My father’s son” — since I have no brothers, that must be ME.

So: “My successor’s father is me.”

Therefore, my successor is my child.

But I have no sons → so must be my daughter.

And since I have no brothers, and my father’s son is me, then yes.

Successor’s father = me → successor is my child → and since no sons, must be daughter.

✔ Answer for Problem 6: My daughter

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Problem 7:
Fast train leaves London for Brighton at 80 mph. Slow train leaves Brighton for London at 35 mph. When they meet, which is farther from London?

When they meet, they are at the SAME point.

So distance from London is the same for both trains at meeting point.

Trick question!

✔ Answer for Problem 7: Neither — they are at the same spot, so equally distant from London

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Problem 8:
Dog runs back and forth between owner and friend. Owner speed 5 km/h, friend 6 km/h, dog 10 km/h. Distance between owner and friend initially 1 km. They move toward each other. Dog starts at owner, runs to friend, back to owner, etc., until they meet. How far does dog run?

Key insight: Instead of tracking each leg of dog’s trip, calculate how long until owner and friend meet, then multiply by dog’s speed.

Owner and friend moving toward each other: relative speed = 5 + 6 = 11 km/h

Initial distance = 1 km

Time to meet = distance / relative speed = 1 / 11 hours

Dog runs continuously at 10 km/h for that time.

Distance dog runs = speed × time = 10 × (1/11) = 10/11 km ≈ 0.909 km

✔ Answer for Problem 8: 10/11 kilometers

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Final Answer:
1. 10 miles each
2. 86 cows, 0 birds
3. 6 items
4. 15
5. 25 years old
6. My daughter
7. Neither — same distance
8. 10/11 km