Mains exams are very important to clear every

**Answer**: Option E

**Explanation**: From both I and II, we find that Rahul is (35 – 25) = 10 years older than his brother, who was born in 1964. So, Rahul was born in 1954.

**2. Question**: What will be the total weight of 10 poles, each of the same weight?

**Statements**: **I.** One-fourth of the weight of each pole is 5 kg.

**II.** Rahul’s brother, who was born in 1964, is 35 years younger to his mother.

**Answer**: Option C

**Explanation**: From I, we conclude that weight of each pole = (4×5) kg = 20 kg.

So, total weight of 10 poles = (20 x 10) kg = 200 kg.

From II, we conclude that:

Weight of each pole = (weight of 3 poles) – (weight of 2 poles) = 20 kg.

So, total weight of 10 pojes = (20 x 10) kg = 200 kg.

**3. Question**: How many children does M have ?

**Statements**: **I.** H is the only daughter of X who is wife of M.

**II.** K and J are brothers of M.

**Answer**: Option D

**Explanation**: From I, we conclude that H is the only daughter of M. But this does not indicate that M has no son. The information given in II is immaterial.

**4. Question**: How much was the total sale of the company?

**Statements**: **I.** The company sold 8000 units of product A each costing Rs. 25.

**II.** This company has no other product line.

**Answer**: Option D

**Explanation**: From I, total sale of product A = Rs. (8000 x 25) = Rs. 200000.

From II, we know that the company deals only in product A.

This implies that sale of product A is the total sale of the company, which is Rs. 200000.

**5. Question**: The last Sunday of March, 2006 fell on which date?

**Statements**: **I.** The company sold 8000 units of product A each costing Rs. 25.

**II.** This company has no other product line.

**Answer**: Option D

**Explanation**: From I, we conclude that 5th, 12th, 19th and 26th of March, 2006 were Sundays.

So, the last Sunday fell on 26th.

From II, we conclude that 31st March, 2006 was Friday. Thus, 26th March, 2006 was the last Sunday of the month.

**Answer**: Option D

**Explanation**: Speed = [60 x \(\frac{5}{8}\)]m/sec = \(\frac{50}{3}\)m/sec

Length of the train = (Speed x Time).

∴ Length of the train = [\(\frac{50}{3}\) x 9]m = 150 m

**2. A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:**

**Answer**: Option B

**Explanation**: Speed of the train relative to man =

(\(\frac{125}{10}\))m/sec.

[\(\frac{25}{12}\) x \(\frac{18}{5}\)]km/hr

= 45 km/hr.

Let the speed of the train be x km/hr. Then, relative speed = (x – 5) km/hr.

∴ x – 5 = 45 ⇒ x = 50 km/hr.

**3. The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:**

**Answer**: Option C

**Explanation**: Speed = [45 x \(\frac{5}{18}\)]m/sec

Time = 30 sec.

Let the length of the bridge be x meters.

Then, \(\frac{130 + x}{30}\) = \(\frac{25}{2}\)

⇒ 2(130 + x) = 750

⇒ x = 245 m.

**4. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:**

**Answer**: Option B

**Explanation**: Let the speeds of the two trains be x m/sec and y m/sec respectively.

Then, the length of the first train = 27x meters,

and length of the second train = 17y meters

∴ \(\frac{27× + 17 y}{2}\) = 23

⇒27x + 17y = 23x + 23y

⇒4x = 6y

⇒4\(\frac{×}{y}\) = \(\frac{3}{3}\)

**5. A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?**

**Answer**: Option B

**Explanation**: Speed = [54 x\(\frac{5}{18}\)]m/sec = 15 m/sec

Length of the train = (15 x 20)m = 300 m.

Then, \(\frac{× + 300}{36}\) = 15

⇒x + 300 = 540

⇒x = 240 m.

**Answer**: Option A

**Explanation**: Required run rate = \(\frac{282 – (3.2 × 10)}{40}\)

\(\frac{250}{40}\) = 6.25

**2. A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?**

**Answer**: Option B

**Explanation**: Required average = \(\frac{67 × 2 + 35 × 2 + 6 × 3}{2 + 2 + 3}\)

\(\frac{134 + 70 + 18}{7}\)

\(\frac{222}{7}\)

= 31 x \(\frac{5}{7}\)

**3. A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?**

**Answer**: Option A

**Explanation**:Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.

∴ Required sale = Rs. [ (6500 x 6) – 34009 ]

= Rs. (39000 – 34009)

= Rs. 4991.

**4. The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?**

**Answer**: Option D

**Explanation**:

Average of 20 numbers = 0.

∴ Sum of 20 numbers (0 x 20) = 0.

It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a).

**5. The average weight of 8 person’s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?**

**Answer**: Option C

**Explanation**: Total weight increased = (8 x 2.5) kg = 20 kg.

Weight of new person = (65 + 20) kg = 85 kg.

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