Quantitative Aptitude - Arithmetic Ability Questions

(Place value of 7)-(face value of 7)
=7000-7=6993.

We are to choose 11 players including 1 wicket keeper and 4 bowlers  or, 1 wicket keeper and 5 bowlers.

Number of ways of selecting 1 wicket keeper, 4 bowlers and 6 other players in 2C1*5C4*9C6 = 840

Number of ways of selecting 1 wicket keeper, 5 bowlers and 5 other players in 2C1*5C5*9C5 =252

Total number of ways of selecting the team = 840 + 252 = 1092

Let original consumption = 100 kg and new consumption = x kg, 

So, 100 * 6 = x * 7.50 => x = 80kg 

Reduction in consumption = 20%.

The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:

= 6*6*6*6=64

n(S) = 64

Let X be the event that all dice show the same face. 

X = { (1,1,1,1,), (2,2,2,2), (3,3,3,3), (4,4,4,4), (5,5,5,5), (6,6,6,6)}

n(X) = 6

Hence required probability = n(X)n(S)=664 =1216

let ABC be the isosceles triangle, the AD be the altitude 

Let AB = AC = x then BC= 32-2x       [because parameter = 2 (side) + Base] 

since in an isoceles triange the altitude bisects the base so 

BD = DC = 16-x 

In a triangle ADC, AC2=AD2+DC2 

x2=82+16-x2 ⇒x=10 

BC = 32-2x = 32-20 = 12 cm 

Hence, required area = 12*BC*AD= 12*12*10 = 60 sq cm

By the rule of alligation:
Cost of 1 kg rice of 1st kind                  Cost of 1 kg rice of 2nd kind 

  Required ratio = 60 : 90 = 2 : 3

Angle traced by hour hand in214 21 hrs = 36012×2140 =157102 

Angle traced by min. hand in 15 min = 36012×150 = 900 

 Required Angle = 157120-900 = 67102

let the sum lent at 5% be Rs.x and that lent at 8% be Rs.(1550-x). then, 

Interest on x at 5% for 3 years + interest on (1550-x) at 8% for 3 years = 300

 x*5*3100+1500-x*8*3100=300 

 x=800

Required ratio =  x : (1550-x) = 800 : (1550-800) = 800 : 750 = 16 : 15