Aptitude and Reasoning Questions

Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.

Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 x 2)/(15 x 14) = 1/35

Probability that both are yellow = ²C₂/¹⁵C₂ = (2 x 1)/(15 x 14) = 1/105

Probability that one blue and other is yellow = (³C₁ x ²C₁)/¹⁵C₂ = (2 x 3 x 2)/(15 x 14) = 2/35

Required probability = 1/35 + 1/105 + 2/35 = 3/35 + 1/105 = 1/35(3 + 1/3) = 10/(3 x 35) = 2/21

Let the total amount in the partnership be 'x'.
Then A's share = x/3
B's share = x/4
C's share = x/5
D's share = x - (x/3 + x/4 +x/5) = 13x/60

A : B : C : D = x/3 : x/4 : x/5 : 13x/60 = 20 : 15 : 12 : 13

A's share in the profit of Rs. 2490 = 20 (2490/60) = Rs. 830.

As both A and B invest the same amounts, the ratio of their profits at the end of the year is equal to the ratio of the time periods for which they have invested.

Thus, the required ratio of their profits = A : B = 8 : 12 = 2 : 3.

Hence, share of A in the total profit = 2 x 25000/5 = Rs.10000

Similarly, share of B in the total profit = 3 x 25000/5 = Rs.15000

Carbon monoxide, when inhaled, combines with haemoglobin of blood to form carboxyhaemoglobin which inhibits the transport of oxygen. 

It means that the first half of the alphabet is interchanged with second half of the alphabet. After making changes, nth letter from the left will be (n + 13)th letter of original series, ie English alphabet; If n is less than 14. But if n is more than 13, nth letter from left will be (n - 13)th letter from left.
In the given equation, we have to find out (13 - 7 =) 6th letter from right => (26 - 6 + 1 =) 21st letter from the left. Hence, required letter's position is more than 13; therefore the required letter is (21 - 13 =) 8th letter from left of original series, ie H.