M4maths Previous Puzzles

28 Oct 2022 Pipes & Cisterns

Pipes A and B are fitted to a tank. A can fill the tank in 1½ hours and capacity of B which is emptying pipe is half that of A. If B is fitted at one-third of the height of the tank from the base and both the pipes are opened simultaneously, then time taken to fill the empty tank is:

OPtion

1) 2 hours
2) 3 hours
3) 1 hour 50 minutes
4) 2 hours 15 minutes
5) 1 hour 45 minutes
6) 2 hours 24 minutes
7) 1 hour 56 minutes
8) 2 hours 30 minutes
9) 2 hours 45 minutes
10) None of these

Solution

Filling capacity of A per hour = 2/3, .'. Emptying capacity of B per hour = (1/2)*(2/3) = 1/3
As B, the emptying pipe is fitted at 1/3 of the height of the tank from base, so the draining will start only after tank is 1/3 full.
Now time taken to fill 1/3 tank by A = (1/3)/(2/3) = 1/2 hrs.
Effective filling per hour after 1/3 tank is full = 2/3 - 1/3 = 1/3
.'. Time required to fill remaining 2/3 tank = (2/3) / (1/3) = 2 hrs
Total time = (1/2 + 2) Hrs = 2 hours 30 minutes
Correct Option 8)

Correct Option: 8 Best Solution (1)

27 Oct 2022 Time & Work

C with his 200% efficiency, can complete 25% of certain work in 12 days. B is 20% more efficient than C. A with 75% efficiency can complete the work in same days as B. If A and B together finish the same work and A gets Rs 10400, then what is the share of B ?

OPtion

1) Rs. 8700
2) Rs. 9200
3) Rs. 9800
4) Rs. 8400
5) Rs. 7800
6) Rs. 9750
7) Rs. 7600
8) Rs. 13870
9) Rs. 11700
10) None of these

Solution

With 200% efficiency C can complete 25% work in 12 days.
⇒ C with 100% efficiency can complete the work in 96 days.
B is 20% more eficient than C, so B can complete the work in 96*(100/120)=80 days.
A with 75% efficiency can complete the work in same days as B ⇒ (100/75)*A=80
.'. A can complete the work in 60 days.
Ratio of efficiencies of A and B = 1/60 : 1/80 = 4 : 3
B's share = (3/4)*10400 = 7800
Correct Option 5)

Correct Option: 5 Best Solution (0)

26 Oct 2022 Ratio and Proportion

Wheat costing Rs. 42 and Rs. 36 per kg is mixed with third variety in the ratio 3:4:5. If this mixture cost Rs. 46.5 per kg, then per kg price of wheat of third variety is:

OPtion

1) 47.6
2) 56.4
3) 49.8
4) 57.6
5) 55.4
6) 54.6
7) 52.2
8) 54.4
9) 54.2
10) None of these

Solution

Let the quantity of 1st, 2nd and 3rd variety be 3 kg, 4 kg and 5 kg respectively, then total quantity=12 kg
Let the cost of 3rd variety be Rs x/kg, then Avg. cost of final mixture = (3*42 + 4*36 + 5*x) / 12 = 46.5
270 + 5x = 558
5x = 288
x = 57.6
Correct Option 4)

Correct Option: 4 Best Solution (3)

25 Oct 2022 Coding & Decoding

If ' BAISAKHI ' is coded as 11092020 and ' NAVRATRI ' is coded as 23194219, then how would ' DIWALI ' be coded ?

OPtion

1) 131224
2) 161824
3) 132421
4) 163221
5) 132124
6) 321321
7) 133224
8) 311224
9) 131242
10) None of these

Solution

When letters from A to Z are numbered from 1 to 26 respectively, then coded number is a sequence of two-digit number obtained by adding pair of position number 1st and last, 2nd and last but 1 and so on ..
BAISAKHI (2, 1, 9, 19, 1, 11, 8, 9) = 11 09 20 20
NAVRATRI (14, 1, 22, 18, 1, 20, 18, 9) = 23 19 42 19
DIWALI (4, 9, 23, 1, 12, 9) = 13 21 24
Correct Option 5)

Correct Option: 5 Best Solution (2)

24 Oct 2022 Arithmetic

On this Diwali, Akash a tech guy, decorated his home by a series of LED lights of three different colours: blue, red and green where he uses total 100 LED lights and also spends exactly Rs. 100 on making this series. If cost of blue LEDs is Rs. 4 for 3, red LEDs Rs. 3 for 9 and green LEDs Rs. 7 for 10, then which of the following can be the number of blue LEDs in the series ?

OPtion

1) 10
2) 62
3) 20
4) 40
5) 63
6) 54
7) 27
8) 14
9) 8
10) None of these

Solution

B + R + G = 100 --- (i) and
B*(4/3) + R*(3/9) + G*(7/10) = 100 ⇒ 40B + 10R + 21G = 3000 ---(ii)
Multiplying eqn. (i) by 10 and subtracting it from (ii), we get 30B + 11G = 2000
B = (2000 - 11G)/30
We get the integer value of B for G=10 and 40, so that count of total lights is 100.
Therefore combinations of Blue, Red & Green are B=63, R=27, G=10 OR B=52, R=8, G=40
Correct Option 5)

Correct Option: 5 Best Solution (1)

21 Oct 2022 Ratio and Proportion

Ratio of income of Jayesh to the expenditure of Suresh is 4:3 and Jayesh spends 85% of his income whereas Suresh spends 90% of his income. If savings of Suresh is Rs. 6000 less than that of Jayesh, then the income of Suresh (in Rs) is

OPtion

1) 76500
2) 90000
3) 67500
4) 76500
5) 88500
6) 75000
7) 60000
8) 81500
9) 105000
10) None of these

Solution

Let income of Jayesh=4x and expenditure of Suresh=3x
Expenditure of Jayesh=85% of 4x=17x/5
Savings of Jayesh=4x - 17x/5=3x/5
Income of Suresh=(100/90)*3x=10x/3
Savings of Suresh=10x/3 - 3x=x/3
Difference of savings of Jayesh & Suresh = 3x/5 - x/3 = 6000
Solving, we get x=22500
.'. Income of Suresh=10*22500/3=75000
Correct Option 6)

Correct Option: 6 Best Solution (1)

20 Oct 2022 Geometry

A boy standing on a ground sees an angle of elevation of 30° to the top of a tower 50 m high . When he started walking towards tower in a straight line, after 3 minutes he observes an angle of elevation of a top of a tower as 60°, then walking speed of a boy is

OPtion

1) 2 km/hr
2) 4 km/hr
3) 1.3333 km/hr
4) 1.5147 km/hr
5) 2.8284 km/hr
6) 2.3094 km/hr
7) 1.1547 km/hr
8) 0.6666 km/hr
9) 1.7320 km/hr
10) None of these

Solution

Let distance walked by boy from starting point where he observes an angle of elevation 30° and the point where he observes angle of elevation 60° be 'x' m and the distance of base of a tower from starting point be 'y' m.
Then, trignometric ratios:
tan 30 = 50/y
1/√3=50/y ⇒ y=50√3 ---(i)
Also, tan 60 = 50/(y-x)
√3=50/(y-x) ⇒ y-x=50/√3 ---(ii)
Substituting value of y from (i) into (ii), we get x=100√3
Now, the distance travelled 'x' in 3 minutes is 100/√3 m, so distance/hr=(60/3)*100/√3=1154.7 m
Speed=1.1547 km/hr
Correct Option 7)

Correct Option: 7 Best Solution (0)

19 Oct 2022 Number Series

What number should replace the question mark in the following series ?
123, 141, 147, 231, 237, ?

OPtion

1) 261
2) 273
3) 312
4) 263
5) 321
6) 357
7) 289
8) 339
9) 269
10) None of these

Solution

Number + (Sum of digits of the number)*Unit digit = Next number
123 + (1+2+3)*3 = 141
141 + (1+4+1)*1 = 147
147 + (1+4+7)*7 = 231
231 + (2+3+1)*1 = 237
237 + (2+3+7)*7 = 321
Correct Option 5)

Correct Option: 5 Best Solution (2)

18 Oct 2022 Percentage

When there is 12.5% fall in price of a chocolate bar, a person is able to purchase 40 more in Rs. 800. The cost (in Rs) of 100 chocolate bars at reduced price is:

OPtion

1) 350
2) 280
3) 320
4) 500
5) 200
6) 420
7) 240
8) 560
9) 250
10) None of these

Solution

Let the initial price of chocolate bar =Rs. x and Number=n
Then, x*n = 800
Also, 0.875x*(n+40) = 800
⇒ 0.875x*n + 35x = 800
0.875*800 + 35x = 800
x = 20/7
Cost of 100 chocolate bar at reduced price = 100*0.875*(20/7) = 250
Correct Option 9)

Correct Option: 9 Best Solution (3)

17 Oct 2022 Ratio and Proportion

In 2022, population of a city is 16 Lakh. Next year in 2023 it increases by 15% but in subsequent year 2024, it decreases by 10%. If this trend continues, then find the number of women in a city in 2027, if ratio of men, women and children after five years is 9:8:10

OPtion

1) 514188
2) 657018
3) 854016
4) 730020
5) 571320
6) 584016
7) 457056
8) 370020
9) 567018
10) None of these

Solution

Total population after 5 years (from 2022 to 2027) = 1600000*(115/100)*(90/100)*(115/100)*(90/100)*(115/100) = 1971054
Given, ratio of men, women, children = 9 : 8 : 10
.'. Number of women = (8/27)*1971054 = 584016
Correct Option 6)

Correct Option: 6 Best Solution (3)