GATE Questions and Answers with Explanation

Q:

Madhu started a business and he invested in 76000, After some month, Amar came to join with him and invest 57000.The end of the year the total profit was divided among them into ratio form 2 : 1.Find after how many months Amar join.

A) 7 months	B) 8 months
C) 3 months	D) 4 months

Answer & Explanation Answer: D) 4 months

Explanation:

we can assume that Amar join into business after x months. So Amar money was invest into (12 – x ) months.

$\frac{76000 \times 12}{57000 \times (12 - x)} = \frac{2}{1}$

--> 912000 = 114000 ( 12 – x ) = 114 ( 12 – x ) = 912

--> x = 4

After 4 months amar join the business.

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Filed Under: Partnership
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Q:

If $\log_{7} (2)$ = m, then $\log_{49} (28)$ is equal to ?

A) 1/(1+2m)	B) (1+2m)/2
C) 2m/(2m+1)	D) (2m+1)/2m

Answer & Explanation Answer: B) (1+2m)/2

Explanation:

$\log_{49} (28) = \frac{1}{2 \log_{7} (7 \times 4)}$

= $\frac{1}{2} + \frac{1}{2} (2 \log_{7} (2))$
= $\frac{1}{2} + \log_{7} (2)$
= $\frac{1}{2} + m$
= $\frac{1 + 2 m}{2}$ .

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Q:

40% of 265 + 35% of 180 = 50% of ?

A) 383	B) 338
C) 84.5	D) 253.5

Answer & Explanation Answer: B) 338

Explanation:

We know that 40% = $\frac{2}{5}$

40% of 265 + 35% of 180 = 50% ?

$\frac{2}{5}$ x 265 + 35% of 180 = 50% ?

We know that (35% of 180 = 180% of 35) & 180% = $\frac{9}{5}$

$\frac{2}{5}$ x 265 + $\frac{9}{5}$ x 35 = 50% ?

106 + 63 = 50% ?

?= 2 x 169 = 338.

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Q:

Pipe A can fill a tank in 16 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes ?

A) 21 min	B) 24 min
C) 20 min	D) 22 min

Answer & Explanation Answer: A) 21 min

Explanation:

Let the pipe B be closed after 'K' minutes.

30/16 - K/24 = 1 => K/24 = 30/16 - 1 = 14/16

=> K = 14/16 x 24 = 21 min.

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Q:

Which tank will fill first?

which_tank_will_be_first_filled1559193031.jpg image

A) 8	B) 7
C) 10	D) 4

Answer & Explanation Answer: C) 10

Explanation:

From the given diagram,

Tank 10 will be first filled because from tank 1 it will go through tank 4 and tank 10.

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Q:

If 25% of a number is subtracted from a second number, the second number reduces to its four-sixth. What is the ratio of the first number to the second number ?

A) 4:3	B) 2:3
C) 3:2	D) 5:3

Answer & Explanation Answer: A) 4:3

Explanation:

Let the numbers be p & q

q-p/4 = 4q/6

=> q-4q/6 = p/4

=> 2q/6 = p/4

=> p/q = 4/3

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Q:

Jagan went to another town covering 240 km by car moving at 60 kmph. Then he covered 400km by train moving at 100 kmph and then rest 200 km he covered by a bus moving at 50 kmph. The average speed during the whole journey was ?

A) 36 kmph	B) 35 kmph
C) 72 kmph	D) 70 kmph

Answer & Explanation Answer: D) 70 kmph

Explanation:

By car 240 km at 60 kmph
Time taken = 240/60 = 4 hr.

By train 240 km at 60 kmph
Time taken = 400/100 = 4 hr.

By bus 240 km at 60 kmph
Time taken = 200/50 = 4 hr.

So total time = 4 + 4 + 4 = 12 hr.
and total speed = 240+400+200 = 840 km
Average speed of the whole journey = 840/12 = 70 kmph.

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Q:

A can do a piece of work in 21 days and B in 28 days. Together they started the work and B left after 4 days. In how many days can A alone do the remaining work ?

A) 14 days	B) 18 days
C) 21 deays	D) 16 days

Answer & Explanation Answer: A) 14 days

Explanation:

Let A worked for x days.

x/21 + 4/28 = 1 => x = 18

A worked for 18 days. So, A can complete the remaining work in 18 - 4 = 14 days.

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