M4maths Previous Puzzles

29 Oct 2020 Profit & Loss

Find the cost price of 1KG of Kaju Katli which is sold for Rs. 990 at a loss of 12%.

OPtion

1) 1100
2) 1025
3) 1075
4) 1125
5) 1175
6) 1000
7) 1145
8) 1150
9) 1225
10) None of these

Solution

If CP 100 SP 88
i.e. When SP 88, CP 100
when SP 880, CP = 100*990/88 = 1125

Correct Option: 4 Best Solution (0)

28 Oct 2020 Mensuration

A string is 148 cm long. It is cut into 3 pieces. The longest piece is 4 times as long as the middle-sized
piece & the shortest piece is 77 cm shorter than the longest piece. Find the length of the shortest piece (in cm).

OPtion

1) 12
2) 21
3) 13
4) 19
5) 28
6) 15
7) 23
8) 25
9) 27
10) None of these

Solution

Let the middle be x CM

Longest piece = 4x cm
Smallest piece = 4x - 77

x+4x+4x-77 = 148
9x = 225
x= 25
shortest piece = 4*25- 77 = 23 cm

Correct Option: 7 Best Solution (4)

27 Oct 2020 Age

A is 20 years older than B who is five times as old as C. The total of the ages of A, B and C is 174 years. What is the value when the square of age of B is multiplied to the sum of ages of A and C ?

OPtion

1) 582500
2) 563500
3) 542500
4) 533500
5) 509600
6) 552550
7) 560500
8) 532500
9) 586500
10)None of these

Solution

Let’s assume Age of B be B years
Age of A = B+20
Age of C = B/5

Total age = B + 20 + B + B/5 = 174
Solving 11B/5 = 154
B = 70
A = 70+20 = 90
C = B/5 = 14

Final Value = (Age of B)^2 * (Age of A + Age of C) = 70^2 * (104) = 509600

Option 5)

Correct Option: 5 Best Solution (0)

26 Oct 2020 Percentage

The price of a plot is decreased from Rupees two crores fifty lakhs to Rupees two crore twenty lakhs. Find the percentage of decrease.

OPtion

1) 14.29
2) 12.00
3) 25.00
4) 20.00
5) 12.50
6) 10.00
7) 15.00
8) 24.00
9) 19.00
10) None of these

Solution

25000000 - 22000000 = 3000000
% = 3000000*100/25000000 = 12%

Correct Option: 2 Best Solution (0)

23 Oct 2020 Heights and Distance

Two persons are on either sides of a tower of height 150 m. The persons observers the top of the tower at an angle of elevation of 45° and 60°. If a car crosses the distance between these two persons in 15 seconds, what is the speed of the car?

OPtion

1) 15.77 km/hr
2) 31.144 km /hr
3) 34.02 km /hr
4) 54.10 km /hr
5) 56.784 m/s
6) 16.784 km /hr
7) 56.10 km /hr
8) 56.784 km /hr
9) 16.63 km /hr
10) None of these

Solution

Let BD be the tower and A and C be the positions of the persons.
Given that BD = 150 m, angle BAD = 45°, angle BCD = 60°

From the right ABD,
tan 45° = BD/BA
=> BD = BA = 150 m

From the right CBD,
tan 60° = BD/BC
=> BC = 150/√3

Distance between the two persons = AC = BA + BC
AC = 150 + 150/√3 = 150 + 86.60 = ~236.60 m

Speed of car = Distance / time = 236.60/15 = 15.77 m/sec = 56.784 km/hr

Option 8)

Correct Option: 8 Best Solution (0)

22 Oct 2020 Arithmetic

Mr. Ramanujam asked his students to find the sum of all pages of their maths book. Chatur gave the answer as 8554.The teacher told him that he has not added one page.
Find the page number which the Chatur forgot to add?

OPtion

1) 72
2) 97
3) 92
4) 98
5) 89
6) 83
7) 81
8) 77
9) 79
10) None of these

Solution

1 + 2 + 3 + .........+n = 8554
⇒ n(n+1)/2 = 8554
⇒ n(n + 1) = 17108
Now, the perfect square closest 17108 is 17161, which is the square of 131.

Sum will be -
131*132/2 = 8646

As the given sum is 8646, so the Chatur forgot to add page number 8646 - 8554 = 92.

Correct Option: 3 Best Solution (3)

21 Oct 2020 Volume

How many cubic meters of earth must be dug out to sink half depth of a well 7350 cm deep and of diameter 9 m.

OPtion

1) 4677.75
2) 4617.75
3) 4627.75
4) 4577.75
5) 4671.75
6) 2398.875
7) 2388.875
8) 2378.875
9) 2338.875
10) None of these

Solution

7350 cm = 73.5 m
Volume of well = Pi*r^2*h
= (22/7)*4.5^2*73.5/2 = 2338.875

Correct Option: 9 Best Solution (1)

20 Oct 2020 Mixture

A mixture contains sugar solution and colored water in the ratio 2 : 3. If 24 liters of colored water is added to the mixture, the ratio becomes 2 : 5. Find the initial quantity of sugar solution in the given mixture (in liters).

OPtion

1) 12
2) 16
3) 15
4) 18
5) 20
6) 24
7) 48
8) 32
9) 36
10) None of these

Solution

The initial ratio is 2 : 3
Let ‘k’ be the common ratio.
=> Initial quantity of sugar solution = 2 k
=> Initial quantity of colored water = 3 k
=> Final quantity of sugar solution = 2 k
=> Final quantity of colored water = 3 k + 24
Final ratio = 2 k : 3 k + 24 = 2 : 5
=> k = 12
Therefore, initial quantity of sugar solution in the given mixture (in liters) = 2 *12 = 24 liter

Correct Option: 6 Best Solution (0)

19 Oct 2020 Area

If the diagonal of a rectangle is 39cm long and its perimeter is 86 cm. Find the area of the rectangle in sq. cm.

OPtion

1) 164
2) 228
3) 328
4) 264
5) 364
6) 128
7) 174
8) 184
9) 154
10) None of these

Solution

Let length = x and breadth = y then

2(x+y) = 86 => x+y = 43
x²+y² = 39² = 1521
now (x+y)² = 43² = 1849
=> x²+y²+2xy= 1849
=> 1521 + 2xy = 1849
=> xy = 164
area = xy = 164 sq.cm

Option 1)

Correct Option: 1 Best Solution (0)

16 Oct 2020 Percentage

A school has 35% students from Maharashtra, out of these 20% are Mumbai students. Find the total percentage of students from Mumbai ?

OPtion

1) 20%
2) 15%
3) 5%
4) 4%
5) 6%
6) 3%
7) 8%
8) 7%
9) 10%
10) None of these

Solution

Total percentage of students from Maharashtra = 35%
Percentage of Mumbai students among 35% of Maharashtra students = 20%
Total percentage of students from Mumbai = 20% of 35 = (35*20)/100 = 7%

Option 8)

Correct Option: 8 Best Solution (2)