CAT Questions

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Let the age of sushma be x and
the age of her son is y
Then five years before x-5=5(y-5) ...(1)
Five years hence x+5 = 3(y+5)-8 .....(2)

By soving (1) & (2), we get
5y - 15 = 3y + 7
y = 11 => x = 35

Therefore, the age of Sushma = 35 and her son = 11.

Since they can do 19 programs in 19 hours, Then 52 programs in 52 hours respectively.
And a 15 min interval
Total time they take to do 52 programs is 52 hours 15 minutes.

Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.
Then, (1/x + 2/x + 3/x) = 1/2
6/x = 1/2 => x = 12
So, B takes 6 hours to finish the work.

Let the average bill paid by twenty members = 'x'

But 19 men paid each = Rs. 70

20th man paid Rs. 90.25 more than the avg bill of 20 = x + 90.25

20x = 19(70) + x + 90.25
19x = 1330 + 90.25
19x = 1420.25
x = 1420.25/19 = Rs. 74.75

But the total bill = 20 x 74.75 = Rs. 1495.

Given 30% of 500

$$\begin{gathered} = 30100 x 500 \\ = 30 x 5 \\ = 150 \end{gathered}$$

Hence, 30% of Rs. 500 = Rs. 150.

      It is a case of shifting as given below:

      1  2  3  4  5                    2  1  3  5  4

      O  F  T  E  N   →  F  O  T  N  E

---------------------------------------------------------------------------

       1  2  3  4  5                   5  4  3  1  2

1.    H  E  A  R  T       →      T  R  A  H  E    

2.    O  P  E  N  S  →  S  N  E  O  P

        1  2  3  4  5         2  1  3  5  4

3.    R  I  S  K  Y  →   I  R  S  Y  K

4.    F  I  R  S  T  →   I  F  R  S  T

Hence option 3 is correct.