It is being given that (2³² + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?

6 x 12 men = 8 x 18 women = 18 x 10 children
? 12 men = 24 women = 30 children
? 2 men = 4 women = 5 children

Now, 4 men + 12 women + 20 children = 4 men + 6 men + 8 men = 18 men
Time to do remaining work in 1 man = (6 x 12 - 18 x 2) = 36 days
? Required number of men to finish the work in 1 days = 36

Solution 1.
Let the question solved correctly by Mohan = X ;
and number of question solved wrongly by Mohan = 30 - X ;
According to the question,
3X - (30 - X) x 2 = 40
? 3x - 60 + 2x = 40
? 5x - 60 = 40
? 5x = 40 + 60 ? x = 100/5 = 20
? Mohan attempted 20 questions correctly .

Solution 2.
Let the question solved correctly by Mohan = X ;
and number of question solved wrongly by Mohan = Y ;
According to given question;
X + Y = 30 ; -----------i
3X - 2Y = 40 ;-------ii

Now multiply the first equation by 2;
we will get
2X + 2Y = 60 ;--------iii
After Add the equation ii and iii , we will get
3X - 2Y + 2X + 2Y = 40 + 60 ;
? 5X = 100 ;
? X = 20;

? Mohan attempted 20 questions correctly .

Concentration of glucose are in the ratio = 1 2 : 3 5 : 4 5

Quantity of glucose taken from A = 1 liter out of 2

Quantity of glucose taken from B = 3/5 x 3 = 1.5 lit

Quantity of glucose taken from C = 0.8 lit

So, total quantity of glucose taken from A,B and C = 3.6 lit

So, quantity of alcohol = (2 + 3 + 1) - 3.6 = 2.4 lit

Ratio of glucose to alcohol = 3.6/2.4 = 3:2

Let quantity of mixture be x liters.

Suppose a container contains x units of liquid from which y units are taken out and replaced by Water. After operations , the quantity of pure liquid =  x 1 - y x n units, Where n = no of operations . 

So, Quantity of Milk =  x 1 - 6 x 2  

Given that, Milk : Water = 9 : 16 

=> Milk : (Milk + Water) = 9 : (9+16)

=> Milk : Mixture = 9 : 25 

 Therefore,  x 1 - 6 x 2 x = 9 25

=> x = 15 liters

Let the tin contain 5x litres of liquids

5 x - 45 x 4 5 5 x - 45 x 1 5 + 45 = 2 5

=> 5(4x - 36) = 2(x + 36)

=> 20x - 180 = 2x + 72

=> x = 14 litres

Hence, the initial quantity of mixture = 70l

Quantity of liquid B

=  70 - 45 x 1 5 + 45

= 50 litres.

Copper in 4 kg = 4/5 kg          and      Zinc in 4 kg = 4 x (4/5) kg

Copper in 5 kg = 5/6 kg          and      Zinc in 5 kg = 5 x (5/6) kg

Therefore, Copper in mixture =  4 5 + 5 6 = 49 30 kg

and  Zinc in the mixture = 16 5 + 25 6 = 221 30kg

Therefore the required ratio = 49 : 221

As water costs free, water sold at cost price of milk gives the profit.

Required profit % = 5/20 x 100 = 5 x 5 = 25%.

The amount of petrol left after 4 operations =  200 × 1 - 40 200 4 =81.92 

Hence the amount of kerosene = 200 - 81.92 = 118.08 liters

Let the initial amount of honey in the jar was K, then 

  512 = K 1 - 1 5 4     ? 20 % = 20 100 = 1 5

        or      

512 = K 4 5 4

Therefore, K = 1250

Hence initially the honey in the jar= 1.25 kg

Rate of rice of quantity 280 kg = Rs. 15.60/kg

Rate of rice of quantity 120 kg = Rs. 14.40/kg

He want to earn a profit of Rs. 10.45/kg

Rate of Mix to sell to get profit of 10.45 =  

$$\begin{gathered} 280 x 15 . 60 + 120 x 14 . 40 280 + 120 + 10 . 45 \\ 4368 + 1728 400 + 10 . 45 \\ = > 15 . 24 + 10 . 45 \\ = 25 . 69 \end{gathered}$$