Brain teasers which require a little math and reasoning are always fun to solve. Here is another such brainteaser. You need to find out that **How many girls have had all these four items** which are bag, shoe, umbrella and ring.

100 girls were attending a party.

85 of them had a red bag,

75 of them have worn brown shoes,

60 of them came with an umbrella and,

90 girls wore a ring. **How many girls have had all these four items?**

Here are your 4 options, let’s see if you can find correct answer:

**A.** 5 **B**. 10 **C.** 20 **D.** 30

**Also Try: **If you like challenging puzzles then try, WHO IS THE COIN THIEF PUZZLE and STRONGBOX 6 DIGIT COMBINATION PUZZLE

**Answer: B. 10**

**Explanation:**

For simplicity let us assume

Girls with umbrella **A=60**

wearing Brown shoes **B=75**

with red bag **C=85**

wearing a ring **D=90**

Solve this brain teaser like below:

### Explanation 1

Now, There must be 60 + 75 – 100 = 35 girls having both A and B

Similarly, 60+85-100=45 girls sharing A and C

Then, 60+90-100=50 girls sharing A and D

Add equation1 (A, B) and equation2 (A, C) and subtract A to find A, B, C

So, 35+45-60=20 girls sharing A, B and C.

Now, in order to find out all girls which share A, B, C and D. We need to add last two equations (A, B, C and A, D and the subtract A)

Finally 20+50-60=10 girls are sharing A,B,C and D.

### Explanation 2

Other way of solving this brain teaser is by assuming in reverse like

Girls with umbrella **A=60.** –> Which means there are 40 girls with no umbrella.

wearing Brown shoes **B=75** –> Which means there are 25 girls with no shoe.

with red bag **C=85** –> Which means there are 15 girls with no bag.

wearing a ring **D=90** –> Which means there are 10 girls with no ring.

If you do the sum of all 4, it would be 40 + 25 + 15 + 10 = 90 which means, there are 90 girls which do not have at least one of these items. So, it gives us our answer 10 girls who have all 4.

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