Quantitative Aptitude - Arithmetic Ability Questions

(2 x 14) men +(7 x 14) boys = (3 x 11) men + (8 x 11) boys

 =>5 men= 10 boys    => 1man= 2 boys

 Therefore, (2 men+ 7 boys) = (2 x 2 +7) boys = 11 boys

( 8 men + 6 boys) = (8 x 2 +6) boys = 22 boys.

 Let the required  number of days be x.

 More boys , Less days     (Indirect proportion)

 More work , More days    (Direct proportion)

 Boys22:11Work1 : 3⋮⋮ 14:x

 Therefore, (22 * 1 * x) = (11 * 3 * 14)

=> x = 21 

Hence, the required number of days = 21

 Lot the total number of workers be v Then,

8OOOv = (12000 * 7) + 6000 (v - 7) <=>  2000v = 42000  <=>  v = 21.

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

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

Area of 4 walls = 2(l+b)h
=2(10+7) x 5 = 170 sq m
Area of 2 doors and 3 windows = 2(1x3)+(2x1.5)+2(1x1.5) = 12 sq m
area to be planted = 170 -12 = 158 sq m

Cost of painting = Rs. 158 x 3 = Rs. 474

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