Quantitative Aptitude - Arithmetic Ability Questions

Let their edges be a and b. Then,

a3/b3 = 1/27 (or) (a/b)3 = (1/3)3 (or) (a/b) = (1/3).

\Ratio of their surface area = 6a2/6b2 = a2/b2 = (a/b)2 = 1/9, i.e. 1:9.

Milk in 1-litre mixture of A = 4/7 litre. 

Milk in 1-litre mixture of B = 2/5 litre. 

Milk in 1-litre mixture of C = 1/2 litre.

By rule of alligation we have required ratio X:Y   

   X                  :                 Y  

  4/7                                2/5  

           \                      /

              (Mean ratio)
                   (1/2) 

           /                      \

 (1/2 – 2/5)     :       (4/7 – 1/2)  

    1/10                      1/1 4 

So Required ratio = X : Y = 1/10 : 1/14 = 7:5

Total ages of 80 boys = 15 x 80 = 1200 yrs.
Total age of 16 boys = 15 x 16 = 240 yrs
Total age of 25 boys = 14 x 25 = 350 yrs.
Average age of remaining boys = 1200 - (240+350) / 80 - (25+15) = 610/41 = 15.25 yrs.

Let ABC be the isosceles triangle and AD be the altitude 

Let AB = AC = x. Then, BC = (32 - 2x). 

Since, in an isosceles triangle, the altitude bisects the base,
so BD = DC = (16 - x).
In triangle ADC,AC2=AD2+DC2 

⇒x2=82+16-x2⇒x=10 

BC = (32- 2x) = (32 - 20) cm = 12 cm. 

Hence, required area =  12*BC*AD=12*12*8=48cm2

Let the number of buffaoes be x and number of ducks be y.

Then 4x + 2y = 2(x + y) + 24  

=> 2x = 24

=> x = 12.

B's 8 days work=(1/12) x 8 = 2/3

Reaining work= 1/3

Now, 1/15 work is done by A in 1 day

Therefore, 1/3 work is done by A in 15 x (1/3) = 5 days

Angle of triangle = 180 × 3/12

= 45 deg

Other angles of the triangle are = 60 deg, 75 deg

Angle of quadrilateral

= 360 - (45 + 60 + 75)

= 180 deg

Therefore, the four angles of the quadrilateral are 45, 60, 75 & 180 degrees.

Hence, the sum of largest and smallest angle of the quadrilateral are 180 + 45 = 225 deg.