CMAT 2021 Slot 2

Anuj takes 1 day to complete 
Bharat takes 2 days 
Chetan takes 4 days and Dhiraj takes 8 days to complete
option A chetan and Dhiraj together will take $$\frac{4\times\ 8}{4+8}=\frac{32}{12}=\frac{8}{3\ }days$$so A is correct.
Now calculating for all we get AB in 2/3 days AC in 4/5 days AD in 8/9 days BC in 8/6 days BD in 16/10 days
So we can say BD is 2nd slowest pair
Hence A and C are correct

we have : 2435753228 
Now here we have 5 odd digits and 5 even digits and total 10 places 
so 5,5,3,3,7 will arrange in 5 places and 2,2,2,8,4 will arrange in 5 places 
we get : total arrangements =$$\frac{5!}{3!}\times\ \frac{5!}{2!\times\ 2!}$$
we get  $$\frac{\left(5!\right)^2}{3!\ \left(2!\right)^2}$$

543 in base 6 expressed in decimal form =5(36)+4(6)+3 =207
317 in base 8 expressed in decimal form = 3(64)+8+7 =207
So statement 1 is correct
Now 16 in base 2 = 10000
32 in base 2 = 100000
Therefore statement 2 is false 
Hence C is the correct answer 

Probability that A releases a mobile = 0.7
Probability that mobile is a success given that it is released by A = 0.8
Probability that mobile is released by A and is success = 0.8*0.7 = 0.56
And probability that mobile is a success and released by B = 0.28
Total probability for success = 0.56+0.28 = 0.84
Now Probability that it is success and is released by A = 0.56/0.84 = 2/3

$$a=\frac{3}{2}b$$
b=$$\frac{3}{4}c$$ and 
d=$$\frac{c}{4}$$
c=4d
Now substituting we get 
$$a=\frac{3}{2}\ \times\ \frac{3}{4}\times\ 4d$$
so we get a=$$a=\frac{9}{2}d$$
a:d=9:2

Let volume be 36 units 
so X fills at 3 units per hour and Y empties at 2 units per hour
Now Tank was filled in 14 hrs so X filled 14*3 =42 units
Now therefore Y emptied 6 units
so it will empty 6 units in 3 hours
so Y will be closed at 11 am

Let price of banana be x 
so price of orange = 3x 
and price of apple will be 6x
Price of 20 bananas , apples and oranges = 200 x  (1)
Now f the price of an apple increases by 10%,
it becomes = 6.6x
so price of 20 apples = 132x
if price of an orange increases by 30% it becomes = 3.9x
so price of 20 oranges = 78x
if price of a banana increases by 20%
it becomes 1.2 x
so price of 20 bananas = 24x
Now total price of 20 bananas , apples and oranges =234x  (2)
So Percentage change in price = $$\frac{234x-200x}{200x}\times\ 100=\ 17$$%

We have 
$$P\left(\frac{R}{100}\right)^2=\ 64$$
And 
$$P\left(1+\left(\frac{R}{100}\right)\right)^{^2}-p\ =\ 704$$
Now dividing both we get :
$$\frac{\left(\frac{R}{100}\right)^2}{\left(1+\frac{R}{100}\right)^2-1}\ =\ \frac{1}{11}$$
Solving we get R/100 = 5
Now substituting we get P = 64*25 = 1600

We have formula :
F = $$I\left(1-\frac{K}{\left(V\right)}\right)^n$$
Here n =3 V =500 k =50 
substituting we get
F/I = 729/1000
Therefore in percentage F = 72.9 percent

Profit share = Investment * Time period 
Now we get ratio of profit of A and B :
$$\frac{50,000\times\ 3\ +\ 40,000\times\ 9}{60,000\times\ 3\ +\ 80,000\times\ 6}$$
we get ratio as $$\frac{510}{660\ }=\ \frac{17}{22}$$