CAT Questions

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12 year old Manish is three times as old as his brother Rajeev who must be 4 years old.
Diff in ages = 8 years.
when Rajeev will become 8 years old, Manish will be 16 yrs old and he will be twice as old as Rajeev.

Ratio of investment of all the three members = (7 x 12) : (9 x 12) : (2/3 x 9 x 6)

= 7 : 9 : 3

Given Rushi's one year profit = Rs. 5600

=> Let the total profit = Rs. P

Then,

P x 7/19 = 5600

Total profit P = 19 x 5600/7 = Rs. 15,200.

(100-x)%  of 88% of 8400 = 6896

=> 100-x10088100x8400 = 6896

=> x = 6.709%

A team of scientists led by Abhay Mudholkar, from CSIR-National Institute of Oceanography (CSIR-NIO) in Goa on February 17, 2017 informed that India’s only live volcano, the barren island volcano in the Andaman and Nicobar Islands has started erupting smoke and lava again. The Barren Island volcano last erupted in 1991 after lying dormant for 150 years. Again the volcano has started showing sporadic activity in small intervals of 5-10 minutes. As per the scientists, during the day only ash clouds were observed, but after sunset red lava foundations were erupting from the crater into the atmosphere and hot lava streamed down the slopes.

Let the numbers be a and b.
We know that product of two numbers = Product of their HCF and LCM
Then, a + b = 55 and ab = 5 x 120 = 600.
=> The required sum = (1/a) + (1/b) = (a+b)/ab
=55/600 = 11/120

55 min. spaces are covered in 60 min.
60 min. spaces are covered in ((60/55) x 60) min = 720/11 min.
Loss in 65 min. = (720/11 - 65 ) = 5/11
Loss in 24 hrs = (5/11 x 1/65 x 24 x 60)min = 1440/143 min.

% of milk in first bottle = 64%

% of milk in second bottle = 100 - 26 = 74%

Now, ATQ

64%            74%
         

         68%

6                    4

Hence, by using allegation method,

Required ratio = 3 : 2