M4maths Previous Puzzles

29 Apr 2022 Number System

The average of squares of five consecutive even natural numbers is 792. The ratio of smallest number to largest number is

OPtion

1) 4 : 5
2) 3 : 4
3) 5 : 6
4) 2 : 3
5) 7 : 8
6) 6 : 7
7) 13 : 15
8) 15 : 16
9) 13 : 17
10) None of these

Solution

Let the five consecutive even numbers be x, (x+2), (x+4), (x+6), (x+8)
Average of squares of these numbers = [x² + (x+2)² + (x+4)² + (x+6)² + (x+8)²] / 5 = 792
x² + x² + 4x + 4 + x² + 8x + 16 + x² + 12x + 36 + x² + 16x + 64 = 3960
5x² + 40x - 3840 = 0
x² + 8x - 768 = 0
(x+32) (x-24) = 0
x = -32, 24
Considering +ve value of a natural number, x=24
.'. The numbers are 24, 26, 28, 30, 32
Required ratio = 24/32 = 3/4

Correct Option: 2 Best Solution (1)

28 Apr 2022 Time and Work

A alone can complete a piece of work in 30 days. B is 50% more efficient than A. With the help of C, together they completes the work in 6 days, then C is ___ efficient than ___ (Fill the blanks with given options separated by ,)

OPtion

1) 66.66% more, A
2) 100% more, B
3) 150% less, A
4) 66.66% more, B
5) 133.33% more, A
6) 166.66% more, B
7) 33.33% more, B
8) 150% more, B
9) 66.66% less, A
10) None of these

Solution

Let A, B and C's 1 day work=100, 150 and x units respectively.
Given, A alone can complete the work in 30 days .'. Total work=30*100=3000 units.
6 day's work of A, B & C = 6*(100+150+x) = 3000
x=250
.'. Ratio of work done by A, B & C = 100 : 150 : 250
⇒ C is more efficient than A and B.
% efficiency of C compared to B = (250/150)*100 = 166.66
% efficiency of C compared to A = (250/100)*100 = 250
⇒ C is 66.66% more efficient than B or 150% more efficient than A.
.'. From the given Option 4) is correct

Correct Option: 4 Best Solution (1)

27 Apr 2022 Time Distance & Speed

Two buses with uniform speeds of 75 km/h and 60 km/h started from stand A at the same time towards stand B. The faster bus after returning from stand B meets slower bus at a distance which is 9 km from stand B. The distance between stand A and B (in km) is

OPtion

1) 72
2) 91
3) 60
4) 71
5) 90
6) 61
7) 80
8) 84
9) 70
10) None of these

Solution

Let the distance between stand A and B = x km
When faster bus with speed 75 km/h covers a distance of (x+9) km, in the same time slower bus with speed 60 km/h covers a distance of (x-9) km
⇒ (x+9)/75 = (x-9)/60
(x+9)/5 = (x-9)/4
4x+36 = 5x-45
x = 81
Correct option 10) None of these

Correct Option: 10 Best Solution (3)

26 Apr 2022 Profit & Loss

A grocery retailer sells vegetable oil in his shop. Due to recent shortfall in the supply of vegetable oil, he increases his selling price by 50% despite the cost price remains same for him due to a fixed price contract. He realizes that his profit have doubled. Find the original profit percent.

OPtion

1) 50%
2) 150%
3) 100%
4) 200%
5) 166.66%
6) 133.33%
7) 66.66%
8) 33.33%
9) 37.50%
10) None of these

Solution

Let the original C.P. be 'x' and S.P. be 'y', then profit = (y-x)
When S.P. = 1.5y and C.P. = x, then profit = (1.5y-x)
Given, New Profit = 2*Original Profit
(1.5y-x) = 2(y-x)
0.5y = x
y/x = 2/1
Original profit % = [(SP-CP)/CP]*100 = [(2-1)/1]*100 = 100%

Correct Option: 3 Best Solution (1)

25 Apr 2022 Simple & Compound Interest

Rajan invested certain amount for 4 years in bank A and received the simple interest Rs. 2800. After that he takes all his amount and invest in bank B for 5 years which offers interest rate double than the bank A. At the end of 5 years, from bank B he receives Rs. 9450 as a simple interest. What was the interest rate that bank A offered to Rajan ?

OPtion

1) 9.75
2) 6.75
3) 8.25
4) 7.50
5) 8.75
6) 10.25
7) 17.50
8) 12.50
9) 10.75
10) None of these

Solution

Let initial Principal=P and rate of bank A = r%
Then, Simple interest for 4 years = P*r*4/100 = 2800
⇒ P*r = 70000
Now, for bank B, Principal amount = (P+2800), Rate=2r%
Simple interest for 5 years = (P+2800)*2r*5/100 = 9450
P*r + 2800r = 94500
70000 + 2800r = 94500
Solving, we get r = 8.75%

Correct Option: 5 Best Solution (2)

22 Apr 2022 Profit & Loss

A seller has two types of items in a store. He allows a discount of 15% on an item whose marked price is Rs. 480 and 25% on an item whose marked price is Rs. 720. If a customer paid total of Rs. 10824 and gets a total discount of Rs. 3096, then how many items of marked price Rs. 720 he has purchased ?

OPtion

1) 9
2) 8
3) 6
4) 7
5) 16
6) 14
7) 10
8) 15
9) 12
10) None of these

Solution

Let the customer purchased 'x' items of marked price 480 and 'y' items of marked price 720
Total Cost = 480x*0.85 + 720y*0.75 = 10824
⇒ 102x + 135y = 2706 ---(i)
Total Discount = 480x*0.15 + 720y*0.25 = 3096
⇒ 18x + 45y = 774 ---(ii)
Solving Eqn (i) & (ii), we get x=8, y=14
.'. Customer purchased 14 items of marked price Rs. 720

Correct Option: 6 Best Solution (1)

21 Apr 2022 Time and Work

B is more efficient than A and they together can complete a work in 18 days. Had A done 60% of the work and then B, the remaining work, then the work would have been completed in 39 days. B alone will complete 60% of the same work in

OPtion

1) 21 days
2) 24 days
3) 30 days
4) 27 days
5) 36 days
6) 45 days
7) 12 days
8) 18 days
9) 15 days
10) None of these

Solution

Let A and B alone takes 'a' and 'b' days respectively, then 1 day work of A & B = 1/a + 1/b = 1/18 ---(i)
When A does 60% or 3/5 work and B remaining 2/5 work, total days required = 39
⇒ (3/5)/(1/a) + (2/5)/(1/b) = 39 ---(ii)
Substituting 1/a=(1/18 - 1/b) from (i) into Eqn (ii), we get (3/5)/[(1/18 - 1/b)] + (2/5)/(1/b) = 39
54b/[5(b-18)] + 2b/5 = 39
54b + 2b(b-18) = 39*5(b-18)
2b² - 177b + 3510 = 0
2b² - 117b - 60b + 3510 = 0
b(2b - 117) - 30(2b - 117) = 0
(b - 30) (2b - 117) = 0
Considering +ve integer value of the days, b=30
⇒ B alone can complete the work in 30 days.
.'. For 60% of the work B require = (60/100)*30 = 18 days.

Correct Option: 8 Best Solution (0)

20 Apr 2022 Area and Volume

A rectangular tank is 20 m long and 21 m deep. If 10,000 liters of water is drawn off the tank, the level of the water in the tank goes down by 1.5 m. How many liters of water can a tank hold ?

OPtion

1) 1,12,000
2) 1,40,000
3) 1,26,000
4) 1,50,000
5) 98,000
6) 84,000
7) 14,000
8) 56,000
9) 70,000
10) None of these

Solution

1 m³ = 1000 litres
.'. 10,000 litres = 10 m³
Let the breadth of a tank = B meters, then volume of water in 1.5 m height = 20*1.5*B = 10 m³
30B=10 ⇒ B=1/3 m
Volume of a tank = L*B*H = 20*(1/3)*21 = 140 m³
Capacity in Litres = 140*1000 = 1,40,000
Option 2) is correct.

Correct Option: 2 Best Solution (1)

19 Apr 2022 Ratio & Proportion

If (a+b):c=11:9 and (b+c):a=5:3, then find a:b:c ​

OPtion

1) 5 : 6 : 18
2) 6 : 7 : 9
3) 15 : 7 : 9
4) 5 : 7 : 18
5) 15 : 6 : 18
6) 10 : 7 : 18
7) 12 : 7 : 9
8) 15 : 7 : 18
9) 10 : 12 : 9
10) None of these

Solution

(a+b)/c = 11/9 ⇒ 9a + 9b = 11c ---(i)
(b+c)/a = 5/3 ⇒ 3b + 3c = 5a ---(ii)
Multiplying Eqn (ii) by 3, 9b + 9c = 15a ---(iii)
Now subtracting Eqn. (i) from (iii), we get 9c - 9a = 15a - 11c
20c = 24a or a/c = 5/6
As (a+b)/c = 11/9 ⇒ a/c + b/c = 11/9
5/6 + b/c = 11/9
⇒ b/c = 7/18
We have a:c = 5:6 and b:c = 7:18.
a : b : c = (5x3) : 7 : 18 = 15 : 7 : 18

Correct Option: 8 Best Solution (2)

18 Apr 2022 Time Distance & Speed

A man travels 840 km in 12 hours, partly by train and partly by car. If he had travelled all the way by train, he would have saved 1/4 of the time he would have taken to travel by car only and would have arrived at his destination 1 hour 30 minutes early. Find the distance he covered while travelling by car.

OPtion

1) 480 km
2) 380 km
3) 520 km
4) 540 km
5) 420 km
6) 360 km
7) 600 km
8) 270 km
9) 300 km
10) None of these

Solution

Total Distance = 840 km.
Total Time taken by Train and Car = 12 Hours
By travelling all the distance by train, he would have reached 1.5 hrs early i.e. He would have taken 12 - 1.5 = 10.5 hrs.
.'. Speed of the train = 840/10.5 = 80 kmph
Time taken by train to travel 840 km = (1 - 1/4)* Time taken by car to travel 840 km = 10.5
⇒ Time taken by car to travel 840 km = 10.5/(3/4) = 14 hrs
.'. Speed of car = 840/14 = 60 kmph
Let the distance covered by car = x km and by train = (840-x) km
Then, x/60 + (840-x)/80 = 12
Solving, we get x=360 km

Correct Option: 6 Best Solution (1)