M4maths Previous Puzzles

07 Jan 2022 ‘KUSUMKHERA’

In how many different ways can the letters of the word ‘KUSUMKHERA’ be permuted?

OPtion

1. 498960
2. 907200
3. 850062
4. 465825
5. 950020
6. 900200
7. 857200
8. 805200
9. 785000
10. None of these

Solution

The word KUSUMKHERA has 10 letters in all. The letter ‘U’ occurs 2 times, the letter ‘K’ occurs 2, and the remaining S, M, H, E, R, A each occur once.
∴ The require number of permutations
= 10! /2!2!1!1! 1!1! 1!1!
= 10! /2!2!
= (10*9*8*7*6*5*4*3*2*1)/2*2
= (10*9*8*7*6*5*2*3)
= 9,07,200

Correct Option: 2 Best Solution (1)

06 Jan 2022 body fall

A body falls 12 m in the first second of its motion, 28 m in the second, 44 m in the third, 60 m in the fourth and so on. How far does it fall during the 16th second of its motion?

OPtion

1. 338
2. 340
3. 334
4. 252
5. 250
6. 278
7. 286
8. 290
9. 258
10. None of the above

Solution

The distances through which the body falls in first, second, third, fourth, ..... seconds form an A.P. 12 + 28 + 44 + 66 + ...
Here, a = 12, d = 16
Distance through which it falls in 16th second = 16 the term of the A.P.
= a + 15d
= 12 + 15 (16)
= 12 + 240 = 252 m

Correct Option: 4 Best Solution (0)

05 Jan 2022 Interest

The discount on a certain sum is due for 3 years, hence it is ₹100. But the interest on the same sum for the same period is ₹110. Find the sum and the interest rate

OPtion

1. 1350
2. 1260
3. 1444
4. 1256
5. 1100
6. 1256
7. 1110
8. 1050
9. 1056
10. None of the above

Solution

We have,
S.I. on T.D. = S.I. - T.D.
= 110 - 100 = ₹10.
∴ Rate (R) = 10 x 100 / (100 x 3)
= 1000 / 300 = 3.33%
and, Sum (A) = S.I. x T.D. / (S.I. - T.D.)
= 110 x 100 / (110- 100)
= 11000 / 10
= ₹1100

Correct Option: 5 Best Solution (0)

04 Jan 2022 Misread

The average weight of 56 students is 56 Kg. It was found later that the figure of 45 Kg was misread as 54 Kg. What is the correct average?

OPtion

1. 56
2. 53.55
3. 52.10
4. 50
5. 54.23
6. 55
7. 60.50
8. 60.88
9. 51.10
10. None of the above

Solution

Correct average
= 56 x 56 - 54 + 45 / 56
= 3127 / 56
= 55.83 Kg

Correct Option: 10 Best Solution (0)

03 Jan 2022 CNG

If the price of CNG increases by 12.5%, find how much per cent its consumption be reduced so as not to increase the expenditure

OPtion

1. 12.5%
2. 13.2%
3. 16.4%
4. 14.25%
5. 11.55%
6. 11.11%
7. 10.50%
8. 10.70%
9. 14.20%
10. None of the above

Solution

Reduction in consumption
= P x100 /(100 +
= 12.5x 100 /(12.5 + 100)%
= 11.11%

Correct Option: 6 Best Solution (4)

01 Jan 2022 Profit and Loss

On selling two items at 40% profit and 20% loss respectively, a shopkeeper gained Rs. 172. If cost prices (in Rs) of these items are (x+220) and (x-150) respectively, then the value of 'x' is:

OPtion

1) 280
2) 344
3) 290
4) 370
5) 180
6) 270
7) 310
8) 220
9) 250
10) None of these

Solution

Total CP = (x+220) + (x-150) = 2x + 70
Total SP = (140/100)*(x+220) + (80/100)*(x-150) = 2.2x + 188
Gain = SP - CP
172 = (2.2x+188) - (2x+70)
0.2x = 54
x = 270
Correct Option 6)

Correct Option: 6 Best Solution (0)

31 Dec 2021 discount

A book seller allowed 18% discount on printed price. He gets 24% commission from publisher. His profit in per cent will be

OPtion

1. 7.8%
2. 6.2%
3. 5.8%
4. 9.3%
5. 9.6%
6. 7.2%
7. 6.8%
8. 8.8%
9. 8.6%
10. None of the above

Solution

Let the selling price = 100
Purchase price after discount = 24% = 100 – 24 = 76
After discount of 10% actual selling price = 100 – 18 = 82
Actual profit = 82 – 76 = 6
Percentage of profit = 6 x 100 /76
= 7.8%

Correct Option: 1 Best Solution (0)

30 Dec 2021 Ticket

Vijay could get equal number of ₹75, ₹95 and ₹100 tickets for a movie. He spent 6210 for all the tickets. How many of each did he buy?

OPtion

1. 12
2. 23
3. 20
4. 18
5. 17
6. 27
7. 31
8. 21
9. 25
10. None of these

Solution

Let, total tickets = t
Then, 75t + 95t+ 100t = 6210
⇒ 270t = 6210
⇒ t = 6210 /270
⇒ t = 23

Correct Option: 2 Best Solution (2)

29 Dec 2021 circular ground

A circular ground of radius 16 m has a path of width 2.8 m around it on its outside. Find the area of the path.

OPtion

1. 304.6
2. 298.8
3. 299.6
4. 300.5
5. 304.25
6. 306.2
7. 310.2
8. 315.5
9. 320.8
10. None of the above

Solution

The area of the circular path = π w(2r + w)
= 22 /7 × 2.8 × (2 × 16 + 2.8)
= 8.8 × (32 + 2.8) = 306.2 m^2

Correct Option: 6 Best Solution (0)

28 Dec 2021 Circle

Find the area of largest circle inscribed in a square of side 112 cm.

OPtion

1. 9866
2. 9842
3. 9870
4. 9888
5. 9856
6. 9850
7. 9840
8. 9360
9. 9690
10. None of the above

Solution

The area of the largest circle
= πa^2 /4
= (22 x112x x112)/ 7 x 4
= 9856 cm^2 .

Correct Option: 5 Best Solution (4)