M4maths Previous Puzzles

13 Jan 2016 Time and distance

A motor boat goes 10 km upstream and back again to the starting point in 55 minutes. Find the speed of the motor boat in still water, if Stream running at 2 kmph

OPtion

1) 18 km/hr
2) 20 km/hr
3) 28 km/hr
4) 26 km/hr
5) 24 km/hr
6) 22 km/hr
7) 16 km/hr
8) 32 km/hr
9) 30 km/hr
10)None of these

Solution

Let he speed of motor boat in still water be x kmph
Speed downstream = (x+2) km/hr, speed upstream = (x-2) km/hr
Therefore 10/x-2 + 10/x+2 = 55/60
11x^2 - 240x - 44 = 0
x = 22
Rate in still water = 22 km/hr
Option 6)

Correct Option: 6 Best Solution (13)

12 Jan 2016 Time and work

8 teachers and 10 children do a school work in the same days as 4 teachers and 16 children do. 1 teacher and 3 children start a school work to finish it in 40 days. After eighteen days, 9/20th part of the school work had been finished. How many children should be increased to make the school work complete in exact time.

OPtion

1) 9
2) 6
3) 3
4) 0
5) 4
6) 5
7) 1
8) 7
9) 8
10) 2

Solution

In 18 days, (9/20)th part of school work is finished
Thus in 1 day, {9/(20*18)}th = 1/40th part of school work is finished
Hence in 40 days, school work will be complete.
No additional children are required.

Option 4)

Correct Option: 4 Best Solution (16)

11 Jan 2016 Number

In (6^41 * 3^56 * 11^7 * 65^9), find the total number of prime factors

OPtion

1) 181
2) 168
3) 157
4) 158
5) 153
6) 171
7) 163
8) 153
9) 161
10)167

Solution

Given exp
(2*3)^41 * 3^56 * 11^7 * (5*13)^9
2^41 * 3^97 * 5^9 * 11^7 * 13^9
41+97+9+7+9 = 163

Option 7)

Correct Option: 7 Best Solution (28)

08 Jan 2016 Percent

Ashok lent Rs.1200 to Bhupesh for 3 years at certain rate of simple interest and Rs.1000 to Chandan for the same time at the same rate. If he gets Rs.50 more from Bhupesh than from Chandan, then the rate percent is

OPtion

1) 31/3 %
2) 32/3 %
3) 20/3 %
4) 13/3 %
5) 19/3 %
6) 25/3 %
7) 10/3 %
8) 16/3 %
9) 29/3 %
10)22/3 %

Solution

1200*3*R / 100 - 1000*3*R / 100 = 50
R = 25/3 %

Option 6)

Correct Option: 6 Best Solution (31)

07 Jan 2016 Radius

The difference between outside and inside surface areas of a tube 28 cm long in 88 cm^2. The total surface area of the tube is 1254 cm^2, find the outer and inner radii of the tube.

OPtion

1) 4.75 cm, 3.25 cm
2) 3.75 cm, 2.75 cm
3) 3.75 cm, 1.25 cm
4) 6.75 cm, 3.25 cm
5) 5.75 cm, 4.25 cm
6) 5.75 cm, 3.25 cm
7) 3.75 cm, 2.25 cm
8) 3.75 cm, 3.25 cm
9) 4.75 cm, 3.25 cm
10)None of these

Solution

Let inner and outer radii be r and R respectively
Difference in curved surface areas = 2 Pi h (R-r)
Total surface area = 2 Pi (R+r)(h+R-r)
we should use difference in surfaces to get (R - r) and substitute it in total surface area formula to get R + r. Then we solve tog get R, r.
we have h = 28
Difference in surface area = 88 cm^2
Total surface area = 1254 cm^2
2 Pi h(R-r) = 88
R-r = 0.5
Aslo 2 Pi (h+R-r)(R+r) = 1254
Using (i) R + r = 7
Solving
R = 3.75 cm
r = 3.25 cm
Option 8)

Correct Option: 8 Best Solution (14)

06 Jan 2016 Time and Work

8 woman and 12 men complete a certain piece of work in 9 days. Each woman takes twice the time taken by a man to finish the work. In how many days will 12 men finish the same work

OPtion

1) 8
2) 9
3) 10
4) 12
5) 14
6) 15
7) 16
8) 18
9) 20
10)22

Solution

2 woman = 1 man
So 8 woman + 12 men = 16 men
Less men, more days (indirect)
12 : 16 :: 9:x
x = 12

Option 4)

Correct Option: 4 Best Solution (25)

05 Jan 2016 Distance

A boy moves 4 meter towards east then 3 meter towards left after then 8 meter towards right then 6 meter towards right then 16 meter towards right. Finally he moves 4 meter towards north followed by 4 meter towards right. What is his distance from the starting point.

OPtion

1) 1 meter
2) 2 meter
3) 3 meter
4) 4 meter
5) 5 meter
6) 6 meter
7) 7 meter
8) 8 meter
9) 9 meter
10)None of these

Solution

a graph to obtain the result.
Ans is 1 m

Option 1)

Correct Option: 1 Best Solution (13)

04 Jan 2016 Sequence

What is the next number of the following sequence
76, 159, 327, 661, 1323, ..........

OPtion

1) 2639
2) 2476
3) 2642
4) 2649
5) 2864
6) 2876
7) 2696
8) 2886
9) 2646
10)2672

Solution

76
76*2 + 7 = 159 [Number*2 + last digit]
159*2 + 9 = 327
327*2 + 7 = 661
661*2 + 1 = 1323
Similarly
1323*2 + 3 = 2649

Option 4)

Correct Option: 4 Best Solution (11)

01 Jan 2016 Time and Distance

Pramod travels for 14 hours 40 min. He covers one half of the journey by train at 60 kmph and the rest half by road at 50 kmph. The total distance traveled by him (in km) is

OPtion

1) 1020
2) 1000
3) 870
4) 940
5) 960
6) 780
7) 800
8) 920
9) 860
10)720

Solution

Let total distance be x km, Then,
x/ 2*60 + 2/ 2*50 = 44/3
5x + 6x = 8800
800

Option 7)

Correct Option: 7 Best Solution (23)

31 Dec 2015 Marks

If Rajendra obtains 10% marks more then Surendra then how many % less marks are obtained by Surendra than Rajendra.

OPtion

1) 9
2) 9.08
3) 10
4) 10.9
5) 10.01
6) 10.1
7) 9.9
8) 9.8
9) 11
10)9.09

Solution

Let marks of Surendra is x
Then according to given condition marks of Rajendra is 1.1x
Difference of marks is 1.1x – x = 0.1x
Hence marks of Surendra are (0.1x/1.1x)*100 = 100/11 = 9.09 % less than marks of Rajendra.

Option 10)

Correct Option: 10 Best Solution (22)