Mixed Quantitative Aptitude Questions Set 52

A boat goes 24 km upstream and 54 km downstream in 6 hrs. In 8 hrs, it can go 36 km upstream and 48 km downstream. The speed (in km/hr) of the boat in still water is:
A) 21
B) 19.5
C) 13.75
D) 18
E) None

View Answer
Option B
Solution:
General method
24/u-v+54/u+v=6—1
36/u-v+48/u+v=8—2
By solving 1 and 2 we got the ans.
Shortcut
U/s…………..D/s……….t
24……………..54………..6 common terms cut= 4 9 1
36……………..48………..8 9 12 2
u/s= (4*12)-(9*9)/(9*2)-(12*1) ==u/s=33/6=5.5
d/s=(4*12)-(9*9)/(4*2)-(9*1) ==d/s=33/1=33
then U=(33+5.5)/2=38.5/2=19.25
V= (33-5.5)/2=27.5/2=13.75
A boat takes 30 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 5 km/hr and the speed of the boat in still water is 10 km/hr, what is the distance between A and B?
A) 146km
B) 150km
C) 180km
D) 190km
E) None

View Answer
Option C
Solution:
Downstream speed= 10+5 = 15
Upstream speed = 10-5 = 5
Now total time is 30 hours
If distance between A and B is d, then distance BC = d/2
Now distance/speed = time, so
d/15 + (d/2)/5= 30
Solve, d = 180 km.
A boat takes 150 min less to travel 40 km downstream than to travel the same distance upstream. The speed of the stream is 4 km/hr. What is the downstream speed?
A) 16 km/hr
B) 12 km/hr
C) 10 km/hr
D) 8 km/hr
E) None

View Answer
Option A
Solution:
Let speed of boat in still water = x km/hr
So speed upstream = x-4, and speed downstream = x+4
Now given:
Time to travel 40 km downstream = time to travel 40 km upstream – 150/60
So 40/(x+4) = 40/(x-4) – 5/2
8/(x-4) – 8/(x+4) = 1/2
x+4 – (x-4)/(x2 – 16) = 1/16
solve, x = 12
so downstream speed = 12+4=16km/hr.
Two pipes can fill a tank with water in 15 and 12 hours respectively and a third pipe can empty it in 4 hours. If the pipes be opened in order at 10, 11 and 1 p.m. respectively, the tank will be emptied at
A) 11 : 40 a.m.
B) 12 : 40 p.m.
C) 4.40p.m.
D) 2.40p.m.
E) None

View Answer
Option C
Solution:
Let tank will be emptied in x hrs after 10am
x/15 + (x-1)/12 – (x-3)/4 =0
x = 40/6 = 6 2/3hrs = 6hrs 40min
Then It will be emptied in 10+6.40=4.40p.m.
Pipes A and B can fill a tank in 10 and 12 hours respectively. Pipe C can empty it in 20 hours. If all the three pipes are opened together, then the tank will be filled in (in hours):
A) 7
B) 5.25
C) 6
D) 7.30
E) None

View Answer
Option D
Solution:
Pipes A,B,C filled together in 1 hour
=1/10 + 1/12 − 1/20 = (11-3)/60 8 /60
Tank filled in 60/8 = 7 ½.
An army lost 10% its men in war, 10% of the remaining due to diseases died and 10% of the rest were disabled. Thus, the strength was reduced to 729000 active men. Find the original strength.
A) 10 Lakh
B) 12Lakh
C) 15Lakh
D) 18Lakh
E) None

View Answer
Option A
Solution:
Let army has 100 men.
10% loss in war, so remained are 90 men
then,10% of 90 died due to diseases, remained 90-9 = 81
then again, 10% of 81 again disabled
So, remained men = 90% of 81
90% of 81 = 729000
(90×81)/100 =729000
1= 10000
100 = 1000000
then total men are 10,00,000.
Weights of two friends P and Q are in the ratio 4:5. If P’s weight is increased by 10% and total weight of P and Q become 82.8 kg, with an increases of 15%. By what percent did the weight of Q has to be increased?
A) 19%
B) 22%
C) 17.5%
D) 12.5%
E) None

View Answer
Option A
Solution:
10……………..x
……….15
x-15 : 15-10
Now, given ratio of P and Q’s weight = 4:5
Hence, (x-15)/(15-10) = 4/5
x = 19%.
A shopkeeper sold a T.V. set for Rs. 17,940 with a discount of 8% and earned a profit of 19.6% . What would have been the percentage of earned if no discount was offered ?
A) 25%
B) 30%
C) 22.5%
D) 40%
E) None

View Answer
Option B
Solution:
SP=Rs 17,940.
MP =17940*100/92=19500
CP=17940*100/119.6=15000
So profit without discount= 19500-15000=4500
Fresh grapes contain 80% water, while dry grapes contain 10% water. If the weight of dry grapes is 500 kg, then what is its total weight (in kg) when it is fresh?
A) 2000
B) 2200
C) 2250
D) 2800
E) None

View Answer
Option C
Solution:
weight of dry grapes = 500 kg
Since dry grapes contain 10% of water, weight of grape pulp in 500 kg of dry grapes
= 90% of 500 = 450 kg
Let x be its total weight when it is fresh.
Fresh grapes contain 80% water. Therefore, 20% of x is 450 kg
100% of x = 450 × 5 = 2250
If a 36 inches long strip cloth shrinks to 33 inches after being washed, how many inches long will the same strip remain after washing if it were 48 inches long?
A) 44 inches
B) 46 inches
C) 55 inches
D) 60 inches
E) None

View Answer
Option A
Solution:
Shrinking of cloth,
= [(36-33)/36]*100.
= 100/12%
Second time the strip shrinks,
= (48*100)/1200 = 4 inches
hence , the cloth remains = 48-4 = 44.

6 Thoughts to “Mixed Quantitative Aptitude Questions Set 52”

LIC AAO 2018

October 18, 2017 at 11:15 am

Dear az please provide weekly CA quiz October 2nd week
1. karthik
  
  October 29, 2017 at 12:20 am
  
  A boat takes 150 min less to travel 40 km downstream than to travel the same distance upstream. The speed of the stream is 4 km/hr. What is the downstream speed?
  
  here: Time to travel 40 km downstream = time to travel 40 km upstream – 150/60
  
  Time to travel 40 km downstream = time to travel 40 km upstream + 150/60
karthik

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