Quantitative Aptitude - Arithmetic Ability Questions

Here, k = 7 and l = 28
Therefore, first number = klx100 % of second number = 7/28 x 100% of second number = 25% of second number.

Arun has completed 13rd of the work in 8 days

Then he can complete the total work in

13 ---- 8

 1 ---- ?

= 24 days

But given Akhil is only 60% as efficient as Arun

Akhil =124×60100=140

Akhil can complete the total work in 40 days

Now, remaining 2/3rd of work can be completed in

 1  ------   40

23 ------   ?  

= 26.66 days.

To get the solution that contains 1 part of milk and two parts of water,
they must be mixed in the ratio as
7x+6x/5y+11y = 1/2
26x = 16y
x/y = 16/26
x/y = 8/13

Let the speed of the boat upstream be p kmph and that of downstream be q kmph

Time for upstream = 8 hrs 48 min = 845hrs

Time for downstream = 4 hrs

Distance in both the cases is same.

=> p x  845= q x 4

=> 44p/5 = 4q

=> q = 11p/5

 Now, the required ratio of Speed of boat : Speed of water current

= q+p2:q-p2

=> (11p/5 + p)/2  : (11p/5 - p)/2

=> 8 : 3

A perfect cube will have prime factors that are in groups of 3; for example 125 has the prime factors 5 x 5 x 5 , and 64 x 125 will also be a cube because its factors will be 4 x 4 x 4 x 5 x 5 x 5

Consider the answer choices in turn.

8 is the cube of 2, and p is a cube, and so the product will also be a cube.

pq will also be a cube as shown above.

pq is a cube and so is 27, but their sum need not be a cube. Consider the case where p =1 and q = 8, the sum of pq and 27 will be 35 which has factors 5 x 7 and is not a cube.

-p will be a cube.

Since the difference between p and q is raised to the power of 6, this expression will be a cube (with cube root = difference squared).

Ratio of investments of A, B & C = 2×6+4×6 : 3×12 : 4×12

= 36 : 36 : 48

= 6 : 6 : 8

But given that the annual profit of B is Rs. 3000

=> 6 ratio = 3000

Then for the total annual profit of partners is

20 ratio = 3000 x 20/6 = 10,000.

Let C = x.
Then B = x/2
and A = x/4

A:B:C = 1:2:4.
C's share Rs.[(4/7)*700) = 400

Let the two numbers be x and y

Given x : y = 3 : 7 .....(1)

Now, x+6 : y+6 = 5 : 9 .....(2)

From (1), x = 3y/7

From (2), 5y - 9x = 24

=> 5y - 9(3y/7) = 24

=> y = 21

=> From(1), x = 9

Hence, the two numbers be 9 and 21