1) A match box measures 4 cm by 2.5 cm by 1.5 cm. What will be the volume of a packet containing 12 such match boxes? How many such packets can be placed in a card board box whose size is 60 cm × 30 cm × 24 cm?
a)240
b)360
c)580
d)560
Click to View Answer
Answer a)240
Volume of a match box
= (4 × 2.5 × 1.5) cm3 = 15 cm3
=Volume of a packet containing 12 match boxes
= (12 × 15) cm3 = 180 cm3.
Now, volume of card board box
= (60 × 30 × 24) cm2 = 43200 cm3.
So, Number of packets that can be put in a
card board = 43200/180 = 240.
2)A rectangular block of ice measures 40cm by 25 cm by 15 cm. Calculate its weight in kg , if ice weighs 9/10 of the weight of the same volume of water and 1 cm3 of water weighs 1 gm?
a)10.5kg
b)13.5kg
c)18.6 kg
d)18.6 kg
Click to View Answer
Answer b)13.5kg
Volume of rectangular block of ice
= 40 × 25 × 15 cm3 = 15000 cm3
Now, weight of 1 cm3 of water = 1 gm
and weight of 1 cm3 of ice = 9/10 th of the weight of 1 cm3 of water.
Weight of 1 cm3 of ice= 9/10 cm
Weight of the rectangular block of ice= (9/10*15000)cm = 13500gm= 13.5 kg
3) A rectangular water reservoir contains 42000 litres of water. Find the depth of the water in the reservoir if its base measures 6 m by 3.5 m.?
a) 2m
b)4m
c)5m
d)7m
Click to View Answer
Answer a) 2m.
Volume of the reservoir = 42000 litres
=42000/1000 m3 [ 1 m3 = 1000 litres]
= 42 m3.
Length of the reservoir = 6 m
Breadth of the reservoir = 3.5 m
Area of the base of the reservoir
= (6 × 3.5) m2 = 21 m2.
But, (Area of the base × Height) = Volume of the reservoir
so, Height or Depth of the reservoir = Volume/Area of the base
= 42/21 = 2m
4)To do a certain work B would take 3times as long as A and C together and C twice as long as A and B together . the 3 men by their united exertions can complete the work in 10 days . how long would each take by himself ?
a)24,40,30,
b)50 ,20 ,60
c)24 , 40, 10,
d)30, 40, 10
Click to View Answer
Answer a) 24,40,30
According to the question , 3times B’s daily work = (A+C)’s daily work
Add B ‘s work both side ,
then ,
4times B’s daily work = (A+B+C)’s daily work = 1/10
B’s daily work = 1/40 …..(1)
also , 2 times C’s daily work =(A+B)’s daily work
add both side C’s daily work,
3times C’s daily work = (A+B+C)’s daily work = 1/10
C’s daily work = 1/30 ……(2)
Now , A’s daily work
= 1/10-(1/40+1/30)= 1/24
A= 24 days , B=40days , C =30 days
5) A shopkeeper offers 5% discount on all his goods to all his costumers . he offers a further discount of 2% on the reduce price to those customers who pay cash. What will you to actually have to pay for an article in cash if its market price is Rs4800?
a)Rs 4500
b)Rs 4563.5
c)Rs 4468.80
d)Rs 4468.85
Click to View Answer
Answer c) Rs 4468.80
We know that MP of article is 4800,
First discount of MP is = 5% of MP, = 5% of Rs 4800
= Rs (5/100×4800)
= Rs 240
Price after discount = Rs4800-Rs 240 =Rs 4560
2nd discount = 2% of Rs4560
= Rs( 4560×2/100)
=Rs 91.20
Price after 2nd discount = Rs4560- Rs 91.20 = Rs 4468.80
6) A motor boat takes 2 hours to travel a distance of 9 km downstream and it takes 6 hours to travel the same distance against the current. The speed of the boat in still water and that of the current (in km/h) respectively are?
a)9, 3
b)8, 5
c)3,1.5
d)6,5
Click to View Answer
Answer C) 3,1.5
Downstream speed,
= 9/2 = 4.5 kmph
Upstream speed,
= 9/6 = 1.5 kmph
Thus, speed of boat in still water,
= (4.5 +1.5)/2 = 3 km/h.
Speed of current = (4.5-1.5)/2 = 1.5 km/h.
7) From two places, 60 km apart, A and B start towards each other at the same time and meet each other after 6 hour. If A traveled with 2/3 of his speed and B traveled with double of his speed, they would have met after 5 hours. The speed of A is?
a)4 km/h
b)6km/h
c)10 km/h
d)12 km/h
Click to View Answer
Answer b) 6km/h
Let the speed of A= x kmph and that of B = y kmph;
According to the question;
Xx6+yx6 = 60
Or, x+y = 10 ——— (i)
And,
{(2x/3)*5}+(2y*5) = 60
Or, 10x+30y = 180;
Or, x+3y = 18; ———- (ii)
From equation (i)x3 – (ii)
3x+3y-x-3y = 30-18
Or, 2x = 12
Hence, x = 6 kmph.
8) Rs. 5887 is divided between Shyam and Ram, such that Shyam’s share at the end of 9 years is equal to Ram’s share at the end of 11 years, compounded annually at the rate of 5%. Find the share of Shyam?
a)3087
b)3452
c)3544
d)3642
Click to View Answer
Answer A)3087
Shyam’s share (1+0.05)9 = Ram’s share × (1 + 0.05)11
Shyam’s share / Ram’s share = (1 + 0.05)11 / (1+ 0.05)9 = (1+ 0.05)2 = 441/400
Therefore Shyam’s share = (441/841) * 5887 = 3087
9)find the least number which upon being divided by 2, 3, 4, 5, 6 leaves in each case a remainder of 1, but when divided by 7 leaves no remainder?
a)351
b)301
c)405
d)300
Click to View Answer
Answer b)301
LCM of(2,3,4,5,6)= 60
So no. will be 60x +1 which is multiple of 7
= 56x+4x+1
4x+1 is multiply of 7 when x=5
put x= 5 in (60x+1) = (60*5+1) = 301
10) A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of man is?
a)12 kg
b)60 kg
c)72 kg
d)96 kg
Click to View Answer
Answer b) 60 kg
Volume of water when boat sinks by 1 cm
V= (3*2*0.01)m^3 = 0.06 m^3
Density of water D (in kg/m^3) = 1000 kg/m^3
Mass of man = Volume of water displaced ×Density of water
M= D*V = (1000*0.06)kg
M= 60 kg
