CAT Questions

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Let the sum be Rs. P. Then,

P1+252x1002-P= 510

P[982- 1] = 510.

Sum = Rs. 1920

So, S.I. = (1920 x 25 x 2) / (2 x 100) = Rs. 480

 H   L   C   N    T    A   U   I   O

      L        N          A        I

There are total 131 letters out of which 7 are consonants and 6 are vowels. Also ther are 2L's , 2N's, 2A's and 2I's.

If all the consonants  are together then the numberof arrangements = 7!2!x 1/2! .

But the 7 consonants  can be arranged themselves in  7!2! x 1/2! ways. 

Hence the required number of ways = 7!2!2!2 = 1587600

Since, in one hour, two hands of a clock coincide only once, so, there will be value.
Required time T = 211H×30 + Ao minutes past H.
Here H - initial position of hour hand = 2 (since 2 O'clock)
A° = Required angle = 0° (Since it coincides)

T = 2112×30 + 0o minutes past 2 

=> 11011 minutes past 2

A book is consists of various chapters, so as the Organization consists of various departments. Therefore if Book is to chapter so organization is to department.

Hence, Book : Chapter :: Organisation : Department.

Radha ----> Radha's mother ------> Mother's mother => Radha's Grand-mother.

Radha's Grand-mother's daughter-in-law ------> Radha's Aunt -----> Radha's Aunt's daughter => Radha's sister-in-law.

Let the total population be 'P'

P x (96/100) = 23040

P = 240 * 100

P = 24000.

Let C1 be the cost price of the first article and C2 be the cost price of the second article.
Let the first article be sold at a profit of 22%, while the second one be sold at a loss of 8%.

We know, C1 + C2 = 600.
The first article was sold at a profit of 22%. Therefore, the selling price of the first article = C1 + (22/100)C1 = 1.22C1
The second article was sold at a loss of 8%. Therefore, the selling price of the second article = C2 - (8/100)C2 = 0.92C2.

The total selling price of the first and second article = 1.22C1 + 0.92C2.

As the merchant did not make any profit or loss in the entire transaction, his combined selling price of article 1 and 2 is the same as the cost price of article 1 and 2.

Therefore, 1.22C1 + 0.92C2 = C1+C2 = 600
As C1 + C2 = 600, C2 = 600 - C1. Substituting this in 1.22C1 + 0.92C2 = 600, we get
1.22C1 + 0.92(600 - C1) = 600
or 1.22C1 - 0.92C1 = 600 - 0.92*600
or 0.3C1 = 0.08*600 = 48
or C1 = 48/(0.3) = 160.
If C1 = 160, then C2 = 600 - 160 = 440.
The item that is sold at loss is article 2. The selling price of article 2 = 0.92*C2 = 0.92*440 = 404.80.