GATE Questions and Answers with Explanation

Q:

The average monthly salary of 24 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 400. What is the manager's monthly salary ?

A) Rs. 8840	B) Rs. 11,500
C) Rs. 12,800	D) Rs. 9450

Answer & Explanation Answer: B) Rs. 11,500

Explanation:

Manager's monthly salary

= Rs. (1900 x 25 - 1500 x 24) = Rs. 11,500

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Q:

Compound interest on a certain sum of money at 20% per annum for 2 years is Rs.5995. What is the SI on the same money at 8% per annum for 6 years ?

A) Rs. 5989	B) Rs. 6540
C) Rs. 7844	D) Rs. 6789

Answer & Explanation Answer: B) Rs. 6540

Explanation:

Given C.I = 5984, R = 20% , T = 2yrs

$C . I = P [(1 + {(\frac{20}{100})}^{2}) - 1]$

5984 = $C.I=P\left [ \left ( 1&amp;plus;\left ( \frac{20}{100}\right )^{2} \right )-1 \right ]$

=> P = (5995x25)/11

P = Rs. 13625

Now S.I = PTR/100

SI = (13625 x 8 x 6)/100 = Rs. 6540

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Q:

A train covered k km at 40 kmph and another 2k km at 20 kmph. Find the average speed of the train in covering the entire 3k km ?

A) 28 kmph	B) 24 kmph
C) 26 kmph	D) 32 kmph

Answer & Explanation Answer: B) 24 kmph

Explanation:

Total time taken = k/40 + 2k/20 hours

= 5k/40 = k/8 hours

Average speed = 3k/(k/8) = 24 kmph.

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Q:

P, Q and R start simultaneously from A to B. P reaches B, turns back and meet Q at a distance of 11 km from B. Q reached B, turns back and meet R at a distance of 9 km from B. If the ratio of the speeds of P and R is 3:2, what is the distance between A and B ?

A) 99	B) 100
C) 89	D) 1

Answer & Explanation Answer: A) 99

Explanation:

Let, Distance between A and B = d

Distance travelled by P while it meets Q = d + 11

Distance travelled by Q while it meets P = d – 11

Distance travelled by Q while it meets R = d + 9

Distance travelled by R while it meets Q = d – 9

Here the ratio of speeds of P & Q => SP : SQ = d + 11 : d – 11

The ratio of speeds of Q & R => SQ : SR = d + 9 : d – 9

But given Ratio of speeds of P & R => P : R = 3 : 2

$\frac{S P}{S R} = \frac{S P}{S Q} x \frac{S Q}{S R} = \frac{(d + 11) (d + 9)}{(d - 11) (d - 9)}$

=> $\frac{(d + 11) (d + 9)}{(d - 11) (d - 9)}$ = 3/2

=> d = 1, 99

=> d = 99 satisfies.

Therefore, Distance between A and B = 99

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Q:

A train 900 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is ?

A) 400 m	B) 300 m
C) 500 m	D) 600 m

Answer & Explanation Answer: A) 400 m

Explanation:

Speed = 78 x 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (900 + x)/60 = 65/3
x = 400 m.

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Q:

In order to maximize his gain, a shopping mall owner decides to reduce the price of electronics goods by 20% and as a result of this, the sales of electronics increase by 40%. If, as a result of these changes, he is able to increase his weekly collection by Rs. 1,05,000, find by what value did the gross collection increase per day?

A) Rs. 14400	B) Rs. 14600
C) Rs. 14800	D) Rs. 15000

Answer & Explanation Answer: D) Rs. 15000

Explanation:

It won't requires that much solving.

Here given the increase in weekly collection by Rs. 1,05,000

That is this increase denotes for all 7 days.

=> Gross Collection increase per day = $\frac{Rs . 1, 05, 000}{7} = Rs . 15, 000$

Hence, the gross collection increase per day = Rs. 15,000.

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Q:

Water is an example of?

A) Element	B) Molecule
C) Compound	D) Both B & C

Answer & Explanation Answer: D) Both B & C

Explanation:

Why Water Is Not an Element :

An element is a substance consisting of only one type of atom. Water consists of two types of atoms: hydrogen and oxygen.

water is both a molecule and a compound :

A compound forms whenever two or more atoms form chemical bonds with each other. The chemical formula for water is H2O, which means each molecule of water consists of one oxygen atom chemically bonded to two hydrogen atoms.

Thus, water is a compound.

It's also a molecule, which is any chemical species formed by two or more atoms chemically bonded to each other. The terms molecule and compound mean the same thing and can be used interchangeably.

Hence, water is both a molecule and a compound.

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Q:

P and Q were assigned to do a work for an amount of 1200. P alone can do it in 15 days while Q can do it in 12 days. With the help of R they finish the work in 6 days. Find the share of R ?

A) 120	B) 240
C) 360	D) 180

Answer & Explanation Answer: A) 120

Explanation:

1/15 + 1/12 + 1/R = 1/6, we got R = 60 (it means R will take 60 days to complete the work alone)

so ratio of work done by P:Q:R = 1/15 : 1/12 : 1/60 = 5 : 4 : 1

so R share = (1/10) x 1200 = 120.

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