Haryana Patwari Exam, 2015

Total Questions: 100

91. Amulya can do a job in 2 days, and Bindu in 6 days. How many days will it take to finish the work if they work together?

Correct Answer: (2) 3/2 days
Solution:(2) Work done in one day by Amulya and Bindu

= 1/2 + 1/6 = (3 + 1)/6 = 4/6 = 2/3

∴ Required time = 3/2 days

92. A train M leaves Meerut at 5 a.m. and reaches Delhi at 9 a.m. Another train N leaves Delhi at 7 a.m. and reaches Meerut at 10:30 a.m. At what time do the two trains cross each other?

Correct Answer: (3) 7:36 a.m.
Solution:Time taken by train M

= 4 hr

Time taken by train N

= 7/2 hr.

∴ Speed ratio = 7/2 : 4 = 7 : 8

∴ Let distance between Meerut & Delhi = 7x × 4 = 28x Km

Let the train meet t hour later than 5 AM.

∴ 7x × t + 8x (t - 2) = 28x

⇒ 7t + 8t - 16 = 28

⇒ 15t = 28 + 16 = 44

t = 44/15 hours

= 2 14/15 hours

= 2 hours 56 minutes.

∴ Required time = 7 : 56 AM

93. Three bells ring at intervals of 9, 12, and 15 minutes, respectively. All the three begin to ring at 9 a.m. At what time will they again toll together?

Correct Answer: (3) 12:00 noon
Solution:Required Time = LCM of 9, 12 & 15.

3 | 9, 12, 15

3, 4, 5

∴ L.C.M = 3 × 3 × 4 × 5

= 180 minutes

= 3 hours

∴ Time by watch = 12 after noon

94. Find two numbers whose Arithmetic mean is 12.5 and Geometric mean is 10.

Correct Answer: (3) 20, 5
Solution:Lets numbers are = a & b

According to question,

Arithmetic means = (a + b) / 2

= 12.5

⇒ a + b = 12.5 × 2 = 25 .....(i)

Geometric mean = √(ab) = 10

⇒ ab = 100 .....(ii)

∴ (a - b)² = (a + b)² - 4ab

= 625 - 400 = 225

∴ a - b = √225 = 15 .....(iii)

Equation (i) + (iii),

2a = 40 ⇒ a = 20

∴ b = 25 - 20 = 5

95. The sum of the series 5 + 13 + 21 + ... + 181 is:

Correct Answer: (1) 2139
Solution:(1) Sₙ = 5 + 13 + 21 + .... + 181

First Number = a = 5

Common difference

= d = 13 - 5 = 8

∴ nᵗʰ number = a + (n - 1)d

⇒ 5 + (n - 1) × 8 = 181

⇒ (n - 1) × 8 = 181 - 5 = 176

⇒ n - 1 = 176/8 = 22

⇒ n = 22 + 1 = 23

∴ Sₙ = n/2 (a + l) = 23/2 (5 + 181)

= 23 × 186 / 2 = 2139

96. Thomas can do a piece of work in 80 days. He works at it for 10 days and then Ajay alone can finish the remaining work in 42 days. In how many days could they complete the work together?

Correct Answer: (3) 30 days
Solution:Work done by Thomas in 10 days = 1/8

Work done by Ajay in 10 days = 1/7

Remaining work = 1 - (1/8 + 1/7)

∴ Time taken by Ajay to complete the work = 7/6 × 42 = 49 days

∴ Work done by Thomas & Ajay in 1 day.

= 1/80 + 1/45 = 3 + 5 / 240 = 8 / 240 = 30

∴ Required time = 30 days

97. Two trains are moving in the same direction at 65 km/h and 45 km/h, respectively. The faster train crosses a man in the slower train in 18 seconds. The length of the first train is:

Correct Answer: (3) 100 m
Solution:Relative speed = 65 - 45 = 20 Km./hr

= 20 × (5/18) m/second

= (50/9) m/second

Required time

= length of first train / relative speed

= 18 ÷ (50/9)

= 1= 18 × (50/9) = 100 meter

98. Smallpox is caused by which virus?

Correct Answer: (2) Variola virus
Solution:Smallpox is an infectious disease caused by variola virus. The last naturally occurring case was diagnosed in October, 1977.

99. The age of the Earth can be determined by which scale/method?

Correct Answer: (2) Radio-Metric Dating
Solution:The best estimate for Earth's age is based on radiometric dating of fragments from the Canton Diablo iron meteorite.

100. Which of the following is a bacterial disease?

Correct Answer: (1) Gonorrhoea
Solution:Neisseria gonorrhoeae, also known as gonococcus is a bacteria, causes the sexually transmitted disease. Sexual transmission is possible through Vagina or oral sex.