CAT Questions

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Given the cost price of the articles = Rs. 450

To get overall 20% gain,

Total Selling Price = (20/100) x 450 = 540

One third of the CP = 1/3 x 450 = Rs. 150

But given 1/3 of articles are sold at 10% loss

S.P of 1/3 of articles = 90% of 150

= 90 x 150/100 = 135

Then, S.P on remaining 2/3 goods must be

= 450 - 135 = 405 ...........(1)

CP on remaining goods

= 2/3 x 450 = 300 ............(2)

Profit = SP - CP = 405 - 300 = 105

Profit %  = (105/300) x 100

= 35%.

Brightness of bulb depends on both voltage and current. The brightness depends on power.

Since we know that  Power (P) = Voltage x Current = V I

So whether you increase the current or the voltage the brightness will increase.

Example Illustration:

 If you connect a long bulb and a round bulb in series, the long bulb glows but the round bulb does not. Both of them have the same current flowing through them (they are in series) but the long bulb has a greater voltage across it because it has more resistance (even though V= IR is not obeyed exactly, voltage drop does depend on the resistance). If you connect a round bulb and a long bulb in parallel, however, it is the round bulb that is brighter because now the voltage across both bulbs is the same but the current is larger through the round bulb (smaller resistance).

Hence, the brightness of a bulb depends on power i.e, both voltage and current.

From the given data,

Let the two gits of a number be x & y

A) x + y = 15

B) x2 - y2 = 45

(x+y) (x - y) = 45

C) x - y = 3

From any 2 of the given 3 statements, we can find that 2 digit number as 

2x = 18 => x = 9

=> y = 6

Hence, 2 digit number is 96.

Any one pair of A and B, B and C or C and A is sufficient to find.

Speed of the stream = 1
Motor boat speed in still water be = x kmph
Down Stream = x + 1 kmph
Up Stream = x - 1 kmph
[35/(x + 1)] + [35/(x - 1)] = 12
x = 6 kmph

Average speed = 2aba+b, here a=25 b=4
= 2 x 25 x 4/(25+4) = 200/29 km/hr.

Distance covered in 5 hours 48 minutes
= Speed x time = (200/29)x (29/5) Distance covered in 5 hours 48 minutes = 40kms.

Distance of the post office from the village = (40/2) = 20 km.

Kunnathur is the Smallest Taluk in Kerala State.

Taluk :

In Kerala, the administrative divisions below the district are called Taluk. There are 77 Taluks in Kerala State.

Eranad is the Largest Taluk in Kerala State.

Palakkad is the Largest District in Kerala State.

Alappuzha is the Smallest District in Kerala State.