Quantitative Aptitude - Arithmetic Ability Questions

The two events mentioned are independent.

The first roll of the die is independent of the second roll. Therefore the probabilities can be directly multiplied.

P(getting first 4) = 1/6

P(no second 6) = 5/6

Therefore P(getting first 4 and no second 6) = 1/6 x 5/6 = 5/36

Let the numbers be x and y. Then, 2x + 3y = 39...(i)and 3x + 2y = 30 ...(ii)

On solving (i) and (ii), we get :  x = 6 and y = 9.

larger number = 9

Choose 1 person for the single room & from the remaining choose 2 for the double room & from the remaining choose 4 people for the four person room, 

 Then, ⁷C₁ x ⁶C₂ x ⁴C₄ 

_{= 7 x 15 x 1 = 105}

If the person who gets 1/4 of the whole gets thrice of what the others get on an average, each one will get =1/3×1/4=112 of the whole.
Therefore, if there are k persons other than the person who gets one-fourth, then 1/4 + k/12 = 1
⇒ k=9

Hence, total number of people = 10.

In this type of questions we need to get the relative speed between them,
The relative speed of the boys = 5.5kmph – 5kmph
= 0.5 kmph

Distance between them is 8.5 km
Time = Distance/Speed
Time= 8.5km / 0.5 kmph = 17 hrs

By mistake = x/10 

Actual value = x * 10 

% Change = 10x-x1010x×100 = 99100×100  = 99% (negative)

Since actual value is greater than the wrong value.