AP Police SI Mains 2019 Arithmetic and Reasoning

Total score of A,B,C is 72×3=216.

after adding D's score total become 70×4=280.

So,D's score=280-216=64.

E's score=64+4=68.

Now ,(A+B+C+D+E)=216+64+68=348.

But total of B,C,D,E is=68×4=272.

So,A's score=348-272=76.

D is correct choice.

Let say, he mixed x of first quality with y of second quality.

Ao,price of x amount of first quality is 15x.

and price of y amount of second quality is 10y.

but he sold (x+y) in 14(x+y).

So,

(15x+10y)1.2=14(x+y)

or,18x+12y=14x+14y.

or,4x=2y.

or,2x=y.

So, x/y=1/2=(1/2)/1.

so,x:y=(1/2):1.

C is correct choice.

10 multiples of

1:1,2,3,4,5,6,7,8,9,10

2:2,4,6,8,10,12,14,16,18,20

And so on but if you observe here,

If 2 is taken out from the series we get,2(1+2+3+4+5+6+7+8+9+10)

Therefore the series comes out to be

S=1(1+2+3+4+…..+10) +2(1+2+3+4+5+6+…+10)+3(1+2+3+4+5+6+…+10)+4(1+2+3+4+5+6+…+10)+5(1+2+3+4+5+6+…+10)+5(1+2+3+4+5+6+…+10)+…….+10(1+2+3+4+5+….+10)

S=(1+2+3+4+5+6+7+8+9+10)(1+2+3+4+5+6+7+8+9+10)

S=((10*11)/2)*((10*11)/2)

S=(110*110)/4

That is the sum comes out to be S

Average is S/100 since there are total 100 numbers

This implies

A=(110*110)/(4*100)

A=121/4=30.25.

A is correct choice.

Copper and Zinc ratio in A and B are 5:2 and 3:4.

According to question,

x+y=28...................(1)

in x quantity of A copper and zinc are as following :

copper=(5x/7) and zinc =(2x/7).

in y quantity of B copper and zinc are as following :

copper=3y/7 and zinc=(4y/7).

So,total copper=(5x/7+3y/7)

and total zinc=(2x/7+4y/7).

According to question:

(5x/7+3y/7)=(2x/7+4y/7)

or,5x+3y=2x+4y.

or,3x=y. Now put this value in (1).

4x=28 or, x=7.

So,y=28-7=21.

So,x:y=7:21=1:3.

D is correct choice.

He needs to supply 7 ltr of Grade II milk : which contain milk:water in 3:2 ratio.

So, He must need $$\left(7\times\frac{3}{5}\right)=4.2$$ ltr of milk.

But ,if we consider only Grade III mixture ,then we have only $$\left(3\times\frac{2}{5}\right)=1.2$$ltr of milk available.

(as Grade III mixed in 2:3 ratio).

So, minimum amount of Grade I milk needed was (4.2-1.2)=3 ltr ,by which he can make

7 ltr of Grade II milk as well as Grade H milk mixtures by adding water to rest of the mixtures.

A is correct choice.

Business man buys two qualities A and B of a product at Rs. 120 per kg and Rs. 60 per kg respectively.

Let say, When he mixes A and B in 1:1, he produces 2kg of 180 Rs. product.

So, 1kg of mixture cost price 90 Rs.

He sold it at 100 Rs/kg.

So,Profit=100-90=10 Rs/kg.

Again ,

Let say, When he mixes A and B in 7:11, he produces 18 kg of (840+660)=1500 Rs. product.

So, 1 kg of mixture cost price $$\frac{1500}{18}$$ Rs.

So, profit=$$100-\frac{1500}{18}=\frac{300}{18}=\frac{50}{3}$$ Rs/kg.

So, percentage increase in profit=$$\frac{\left(\frac{50}{3}-10\right)}{10}\times100=\frac{20}{30}\times100=\frac{200}{3}.$$

D is correct choice.

Let say, liquid A and B in the jar are 4k and k.

if 10 litter of mixture is taken ,then amount of A and B in the jar would be (10×4/5) and (10×1/5) or 8 litter and 2 litter respectively.

So,in the mixture A will be left 4k-8 and B will be left k-2.

Now if we add 10 litter of B ,then new amount of B will be=k-2+10=k+8.

So,

(4k-8)/(k+8)=2/3.

Or,12k-24=2k+16.

or,10k=40.

or,k=4.

So, initially amount of A was 4×4=16 litter.

D is correct choice.

Let say ,CP of 32 ltr juice is 100 Rs and x ltr water to be mixed in the juice.

Then (32+x) ltr of juices selling price is$$=\frac{100\left(32+x\right)}{32}.$$

So, $$\frac{100\left(32+x\right)}{32}=125.$$

or,$$100x+3200=4000.$$

or,$$100x=800.$$

or,$$x=8.$$

A is correct choice.

A can fill tank in(1/4)hr=15 min.

and B can fill tank in (1/6)hr=10 min.

C can empty the 7 litter in 1 min.

So, in 1 min A can fill V/15 part of tank.

in 1 min B can fill V/10 part of tank.

1 min A,B and C can empty (7-V/15-V/10)

=(210-5V)/30.

=(42-V)/6.

=(7-V/6).

in 120 min it will empty (840-20V).

So, (840-20V)=V.

or,21V=840.

or,V=40.

So,D is correct choice.

Let us call the Pipe A.

Pipe A fills the cistern in 5hrs

so in one hr Pipe A fills 1/5th of the cistern.

However with the leak it takes 6hrs for Pipe A to fill the cistern.

Hence in one hour the cistern will have 1/6th left in.

So the difference between not leaking and leaking is 1/5 - 1/6= 1/30th of the cistern

this is amount of leak per hour.

Hence it will take 30 hours to fully empty the cistern.

A is correct choice.