Quantitative Aptitude - Arithmetic Ability Questions

ab×bc=45×1516=34=16-916+9

=725

Let A be the event of A will tell truth. B be the event of B tell truth

 P(A)=23,P(Ac)=1-P(A)=13

P(B)=45,P(Bc)=1-P(B)=15 

When both agree then they say true or they say false together, that is 

 A∩B or Ac∩Bc

Also these events will be mutually exclusive :

 P(A∩B)+P(Ac∩Bc)=P(A)P(B)P(C)=23*45+13*15=35

For solving this problem first we would break the whole range in 5 sections

1) From 1 to 9
Total number of zero in this range = 0

2) From 10 to 99
Total possibilities = 9*1 = 9 ( here 9 is used for the possibilities of a non zero integer)

3) From 100 to 999 - three type of numbers are there in this range
a) x00 b) x0x c) xx0 (here x represents a non zero number)
Total possibilities
for x00 = 9*1*1 = 9, hence total zeros = 9*2 = 18
for x0x = 9*1*9 = 81, hence total zeros = 81
similarly for xx0 = 81
total zeros in three digit numbers = 18 + 81 +81 = 180

4) From 1000 to 9999 - seven type of numbers are there in this range
a)x000 b)xx00 c)x0x0 d)x00x e)xxx0 f)xx0x g)x0xx
Total possibilities
for x000 = 9*1*1*1 = 9, hence total zeros = 9*3 = 27
for xx00 = 9*9*1*1 = 81, hence total zeros = 81*2 = 162
for x0x0 = 9*1*9*1 = 81, hence total zeros = 81*2 = 162
for x00x = 9*1*1*9 = 81, hence total zeros = 81*2 = 162
for xxx0 = 9*9*9*1 = 729, hence total zeros = 729*1 = 729
for xx0x = 9*9*1*9 = 729, hence total zeros = 729*1 = 729
for x0xx = 9*1*9*9 = 729, hence total zeros = 729*1 = 729
total zeros in four digit numbers = 27 + 3*162 + 3*729 = 2700
thus total zeros will be 0+9+180+2700+4 (last 4 is for 4 zeros of 10000)
= 2893

Let the tin contain 5x litres of liquids

5x - 45 x 455x - 45 x 15 + 45 = 25

=> 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 15 + 45

= 50 litres.

Face value of the bill = Rs. 6000.

Date on which the bill was drawn = July 14 at 5 months. Nominally due date =                  December 14.

Legally due date = December 17.

Date on which the bill was discounted = October 5.

Unexpired time  : Oct.               Nov.                Dec.

                                 26  +               30  +              17     = 73 days  =1/ 5Years

 B.D. = S.I. on Rs. 6000 for 1/5 year

= Rs.   (6000 x 10 x1/5 x1/100)= Rs. 120.

T.D. = Rs.[(6000 x 10 x1/5)/(100+(10*1/5))]

            =Rs.(12000/102)=Rs. 117.64.

B.G. = (B.D.) - (T.D.) = Rs. (120 - 117.64) = Rs. 2.36.

Money received by the holder of the bill = Rs. (6000 - 120) = Rs. 5880.

P=2(l+b)

l=4b

Ratio of the share of a lady, a gents and a girl is 7 : 4 : 3
No of ladies, gents and girls are 5, 3, 3
Thus effective ratio of ladies, gents and girls is 7 x 5 : 4 x 3 : 3 x 3 = 35 : 12 : 9
so part of gents = (12/56) x 7444 = Rs. 1595.142
so part of 1 gents = 1595.142/3 = Rs. 531.71.

x = y  <=> 1 - q =  2q  + 1  <=> 3q  = 0 <=> q = 0.