M4maths Previous Puzzles

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)

15 Oct 2020 Number of Cans

Chintu works at a soft drink company and was arranging some particular number of cylindrical aluminium soft drink cans in a square box but the box became full and there were 14 cans remaining to be put in. Then, he started arranging all Cans in a rectangular box where he could arrange 8 cans more along the length than the breadth after putting all the cans in the rectangular box. He found out that there was still space left for another 9 cans. What is the number of cans Chintu had if it is known that the number of cans were more than 10 and no can was put on top of another can?

OPtion

1) 44
2) 25
3) 16
4) 39
5) 36
6) 33
7) 45
8) 40
9) 43
10) None of these

Solution

In a square box the number of cans arranged along the length and breadth would be same.
In case of rectangular box, lets assume that number of cans along breadth is x then number of boxes along the length would be x+6
Total number of cans the rectangular box can take = x*(x+8)
Total number of cans Chintu was able to put in the rectangular box (as some empty space was remaining ) = x*(x+8) - 9 --- (i)


Given that the number of cans are more than 10, hence 2 & 3 cans along the length are ruled out

Lets try with 4 cans along length of square box, total cans in box would be 16
Total number of cans which Chintu has = 16+14 = 30 ---- (ii)
(i = (ii)
x*(x+8) - 9 = 30
=> x^2 + 8x = 39
Trying to solve we realize that there is no such whole number which x can take

Lets try with 5 cans along length of square box, total cans in box would be 25
Total number of cans which Chintu has = 25+14 = 39 ---- (ii)
(i = (ii)
x*(x+8) - 9 = 39
=> x^2 + 8x = 48
Solving we get x = 4

So total number of cans which Chintu had = x*(x+8) - 9 = 4(4+8) - 9 = 39

Correct Option: 4 Best Solution (1)

14 Oct 2020 Decode

If SWEET = 65337 and SALTY = 64179 then the code for TASTY would be =?

OPtion

1) 71679
2) 72679
3) 74619
4) 74879
5) 74678
6) 74679
7) 74579
8) 74379
9) 74179
10) None of these

Solution

AS SWEET is coded as "65337" and SALTY is coded as "64179"
So S is coded as 6, W as 5, E as 3, T as 7
and A as 4, L as 1, T as 7, Y as 9

So code for TASTY would be = 74679

Correct Option: 6 Best Solution (0)