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

Let’s solve each question one by one, step by step.

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Question 1:
Two people walk in opposite directions. Each walks 6 miles forward, then turns right and walks 8 miles. How far is each from the starting point?

Think of it like this:
Each person makes a right-angle turn — so their path forms a right triangle.
- First leg: 6 miles (forward)
- Second leg: 8 miles (right turn → perpendicular to first)

We can use the Pythagorean theorem:
Distance = √(6² + 8²) = √(36 + 64) = √100 = 10 miles

So each person is 10 miles from start.

✔ Answer: b) 10 miles 10 miles

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Question 2:
Cows and birds. Total eyes = 172, total legs = 344.

Note: Every animal has 2 eyes → So total animals = 172 ÷ 2 = 86 animals

Let cows = C, birds = B
C + B = 86 → Equation 1

Legs: Cows have 4 legs, birds have 2 → 4C + 2B = 344 → Equation 2

Simplify Equation 2: divide by 2 → 2C + B = 172

Now subtract Equation 1 from this:

(2C + B) - (C + B) = 172 - 86
→ C = 86

Then B = 86 - C = 0? That can’t be right… Wait, let’s check again.

Wait — if C = 86, then legs = 4×86 = 344 → which matches! And birds = 0.

But that means no birds? Let’s verify:

Eyes: 86 animals × 2 = 172 ✔️
Legs: 86 cows × 4 = 344 ✔️

So yes — he has 86 cows and 0 birds.

But maybe the problem expects both? Let me double-check math.

Alternative approach:

From C + B = 86 → B = 86 - C

Plug into legs: 4C + 2(86 - C) = 344
→ 4C + 172 - 2C = 344
→ 2C = 344 - 172 = 172
→ C = 86 → B = 0

Yes, correct. He has only cows.

✔ Answer: 86 cows, 0 birds

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Question 3:
14 red socks, 14 white socks. Minimum number to take to guarantee a matching pair?

Worst case: You pick one red, one white → still no pair.

Next sock (third one) must match one of them.

So minimum = 3 socks

✔ Answer: 3

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Question 4:
When a number is multiplied by 13, it becomes greater than 105 by an amount equal to how much it was less than 105 before.

Let the number be x.

Before multiplying: difference from 105 = 105 - x
After multiplying: 13x - 105

According to problem:
13x - 105 = 105 - x

Solve:

13x + x = 105 + 105
14x = 210
x = 210 ÷ 14 = 15

Check:
15 × 13 = 195
195 - 105 = 90
105 - 15 = 90 → matches!

✔ Answer: 15

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Question 5:
Time left = 1/5 of time already completed.

Let time completed = T
Then time left = T/5

Total exam time = T + T/5 = (6T)/5

But we don’t know total time. However, the question asks “how much time is left?” — but without total time, we can only express it as fraction.

Wait — perhaps they want ratio or expression? But likely, we need to assume something.

Actually, re-read: “the teacher answered that the amount of time left is 1/5 of the time already completed.”

So if time completed = 5 parts, time left = 1 part → total = 6 parts.

So time left = 1/6 of total time.

But question says “How much time is left?” — without total time given, maybe answer is “1/5 of the time already spent” — but that’s not numerical.

Wait — perhaps we’re missing context? Or maybe it’s asking for ratio?

Looking back at original: “How much time is left?” — probably expects fractional answer relative to completed time.

But since no numbers, maybe answer is just “1/5 of the time already completed”.

But that seems odd. Perhaps in context of test, they expect you to say “if completed time is 5 units, left is 1 unit” — but still.

Wait — maybe I misread. Let me see.

Actually, perhaps the question implies we can find actual time? No, no total given.

Hmm. Maybe it's a trick — answer is simply “1/5 of the time already completed”.

But let’s think differently. Suppose total time is fixed? Not stated.

Perhaps the answer is meant to be expressed as a fraction of total time.

If time completed = 5x, time left = x → total = 6x → time left = x = 1/6 of total.

But question doesn’t specify.

Looking at similar problems — often they expect you to say time left is 1/5 of completed, so if completed is 50 mins, left is 10, etc. But here no numbers.

Wait — perhaps the question is incomplete? Or maybe in original doc there was more?

Given what’s written, best answer is: Time left is 1/5 of the time already completed.

But since it’s multiple choice? No, this one isn’t multiple choice.

In the image, Q5 has no options — so we write answer.

I think safest is to say: If time completed is T, time left is T/5.

But perhaps they want numerical value? Impossible without total.

Wait — maybe I missed something. Re-read:

“When asked in an exam how much time is left, the teacher answered that the amount of time left is 1/5 of the time already completed. How much time is left?”

This is ambiguous. But in many such puzzles, they imply that you can find the fraction of total time.

So: Let time completed = 5k, time left = k → total = 6k → time left = k = 1/6 of total time.

But question doesn’t ask for fraction of total — it asks “how much time is left?” — which is vague.

Perhaps in context, answer is “1/5 of the time already spent”.

I think for now, I’ll go with: The time left is one-fifth of the time already completed.

But let’s move on and come back.

Actually, looking at standard versions of this puzzle — often the answer is expected as a fraction of total time.

For example, if total time is 60 minutes, completed = 50, left = 10 → 10 is 1/5 of 50, and 10 is 1/6 of 60.

So time left = 1/6 of total time.

But since total not given, perhaps answer is “1/6 of the total exam time”.

I think that’s reasonable.

✔ Answer: 1/6 of the total exam time

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Question 6:
Two cyclists going opposite directions at 10 mph each. When 50 miles apart, housefly starts from first cyclist, flies to second at 16 mph, then back, etc. How far does fly travel in 1 hour?

Key insight: The fly is flying continuously for 1 hour at 16 mph.

Regardless of back and forth, distance = speed × time = 16 mph × 1 h = 16 miles

The cyclists’ movement affects when they meet, but the fly flies for exactly 1 hour at constant speed.

So answer is 16 miles.

✔ Answer: 16 miles

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Question 7:
“My successor’s father is my father’s son. I don’t have any brothers or sons. Who is my successor?”

Break it down:

“I don’t have any brothers or sons” → so “my father’s son” must be ME (since no brothers).

So: “My successor’s father is me.”

Therefore, my successor is my child.

But I have no sons → so must be daughter.

Also, “successor” could mean heir, child, etc.

Options: a) Nephew b) Niece c) Daughter d) Myself

Since I have no sons, and successor’s father is me → successor is my daughter.

✔ Answer: c) Daughter

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Question 8:
Fast train leaves London for Brighton at 80 mph. Slow train leaves Brighton for London at 35 mph at same time. When they meet, which is farther from London?

They are moving toward each other. When they meet, they are at the same point.

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

Answer: Neither — they are at same location.

But options? In image, no options listed for Q8 — wait, in user input, Q8 has no choices shown, but in text it says “which is farther from London?”

Logically, when two objects meet, they are at same position → same distance from London.

So answer: Both are equally far from London.

But perhaps trick question? No.

✔ Answer: They are at the same distance from London.

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Question 9:
Girl walks 6 km/h, boy 5 km/h, dog runs back and forth between them at 10 km/h for 1 hour. How far does dog travel?

Same as Q6 — dog runs continuously for 1 hour at 10 km/h.

Distance = 10 km/h × 1 h = 10 km

The walking speeds of girl and boy don’t matter — dog’s total distance depends only on its own speed and time.

✔ Answer: 10 km

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Now, compiling all answers:

1. b) 10 miles 10 miles
2. 86 cows, 0 birds
3. 3
4. 15
5. 1/6 of total exam time (or time left is 1/5 of time completed — but I'll go with fraction of total)
6. 16 miles
7. c) Daughter
8. Same distance from London
9. 10 km

But for Q5, to be precise, since no total time given, perhaps best to state relationship.

However, in many sources, for such question, answer is "1/6 of the total time".

Similarly, for Q8, answer is they are at same point.

Now, for final output, since user didn't specify which question, but uploaded whole sheet, I should provide all answers.

But the instruction says "solve the problem" — singular — but image has multiple.

Perhaps user wants all solved.

Given that, I'll list all answers clearly.

Final Answer:
1. b) 10 miles 10 miles
2. 86 cows and 0 birds
3. 3
4. 15
5. \frac{1}{6} of the total exam time
6. 16 miles
7. c) Daughter
8. Both trains are at the same distance from London when they meet.
9. 10 km