Aptitude and Reasoning Questions

Any number divisible by 9 is also divisible by 3.

If there are total 100 candidates,
40 candidates are really capable and
60 candidates are incapable.
Of the candidates who are really capable = 80%
40*(80/100)=32 pass the test and
of the incapable= 30%
60*(30/100)=18 pass the test.
Total candidates who passed the test = 32+18 = 50
The proportion of the really capable students who can pass the test to the total students who can pass = 32/50 = 16/25.

Mercury is the only liquid metal in the group.

E is the daughter of C and D is the son of C. So, F, who is the maternal uncle of D, is also the maternal uncle of E. 

Thus, E is the niece of F. 

Given share of L is 2/7 th of profit. Then, their profits are divided in to 5:2 ratio.

Ratio of K and L is

16000×8x×4=52

x = Rs. 12,800.

Clearly, though all the alternatives may form a part of the atmosphere, the air is the most vital part, without which there can be no atmosphere. So, the answer is (b).

From above diagram
AC represents the hill and DE represents the tower

Given that AC = 100 m

angleXAD = angleADB = 30° (∵ AX || BD )
angleXAE = angleAEC = 60° (∵ AX || CE)

Let DE = h

Then, BC = DE = h, AB = (100-h) (∵ AC=100 and BC = h), BD = CE

tan 60°=AC/CE => √3 = 100/CE =>CE = 100/√3 ----- (1)

tan 30° = AB/BD => 1/√3 = 100−h/BD => BD = 100−h(√3)
∵ BD = CE and Substitute the value of CE from equation 1
100/√3 = 100−h(√3) => h = 66.66 mts

The height of the tower = 66.66 mts.

Money lent to A+B = (300 + 540) = Rs. 840 

Amount received = Rs. 1032 

Interest received = Rs. 1032 - Rs.840 = Rs. 192

Interest on Rs. 300 lent to A for 1 year = 300×1×4100 = Rs. 12 

Interest on Rs.540 lent to B for 1 year = 540×6×1100 = Rs. 36 

Total yearly interest = Rs.(12+36) = Rs.48 

If interest is Rs. 48, time = 1 year 

If interest is Rs. 192, time =  192/48 = 4 years