Official Quant thread for CAT 2013

@sumit99 said:
If on an item a company gives 25% discount, they earn 25% profit. If they now give 10% discount then what is the profit percentage.
Profit = 50%

Approach:

Let CP = 100
SP = 125
MP = 125/75*100 = 166.67

Now after giving 10% of discount SP will be 166.67 - 0.10*166.67 = 150

So profit now is 50%

X is standing at an intersection where two roads intersect at right angles. He observes through his binoculars that two cars start moving towards the intersection at the same time along the intersection at the same time along these two roads. One of them is moving at a speed of 13.333 m/s and starts at a point 40 km form the intersection . The second car is moving at 10m/s and starts at a point 50km from the intersection . In how many min from the start will the distance between the two be minimum?

a 83 b 62 c 50 d 1and 3

@IIM-A2013 said:
In learning experiment at stanford university it was found that the square of the inverse of learning time varies directly as the age of a rat in weeks, while the inverse of learning time and complexity index of the maze are directly related. If the age of the rat in the second trial of the experiment is 40% more than in the first trial and the learning time is 16.67% less, then find change in complexity index of the maze:- a. +10% b. +5% c. +1% d. -5%
bro is the answer a?
@iLoveTorres it's b in book. tell your approach

my approach is vague. it would be better to wait for someone to give a proper logical approach


@IIM-A2013 said:
@Todd approach 16 is correct
Lets take one way calculation ....

It takes 7 days + 1 min. So a train when leaves from station A on Monday reaches station B on next Monday 12:01. So this train can be used from station B to station A on Tuesday latest.
Thus in meanwhile from Station A 8 trains have to depart to station B.
Similar is the case with Station B

So total train used by both station is 16

Hope this is clear.
A shopkeeper has 100 kg of wheat flour which he sells in packets of 5 kg at cost price. Every time after selling one packet, he adds an equal amount of husk to the leftover flour. What percentage profit does the shopkeeper earn on the packet sold to the 4th customer?
@IIM-A2013 said:
X is standing at an intersection where two roads intersect at right angles. He observes through his binoculars that two cars start moving towards the intersection at the same time along the intersection at the same time along these two roads. One of them is moving at a speed of 13.333 m/s and starts at a point 40 km form the intersection . The second car is moving at 10m/s and starts at a point 50km from the intersection . In how many min from the start will the distance between the two be minimum? a 83 b 62 c 50 d 1and 3
ans c?
@iLoveTorres said:
ans c?
its b
@Ani1308 said:
9:4?
explain
@hippophobia said:
explain
already explained buddy..go through the prvious page..
@hippophobia said:
explain
@Ani1308 approach
v =k × d^2 × t -- given

v1 = k × 4^2 × t1
v2= k × 3^2 × t2

as v1 = 4v2
solve them and t1:t2= 9:4
@shinoda said:
A shopkeeper has 100 kg of wheat flour which he sells in packets of 5 kg at cost price. Every time after selling one packet, he adds an equal amount of husk to the leftover flour. What percentage profit does the shopkeeper earn on the packet sold to the 4th customer?
is it around 28%
@shinoda said:
A shopkeeper has 100 kg of wheat flour which he sells in packets of 5 kg at cost price. Every time after selling one packet, he adds an equal amount of husk to the leftover flour. What percentage profit does the shopkeeper earn on the packet sold to the 4th customer?
after 1st customer

95 kg pure, 5 kg husk
2nd customer
95-95/20=90.25 pure....5-5/20 +5=9.75 kg husk

3rd customer..

90.25-(0.9025*5) pure...9.75-(0.0975*5)+5 husk
85.7375 pure 14.2625 husk


on 4th cutsomer he will earn a profit =(100-85.7375)/85.7375=14.2625/85..7375=16.66%??

@IIM-A2013 said:
In learning experiment at stanford university it was found that the square of the inverse of learning time varies directly as the age of a rat in weeks, while the inverse of learning time and complexity index of the maze are directly related. If the age of the rat in the second trial of the experiment is 40% more than in the first trial and the learning time is 16.67% less, then find change in complexity index of the maze:- a. +10% b. +5% c. +1% d. -5%
I am not getting what is wrong in my approach. let me know where I am doing mistake

Now we know

CI = Constant/ (T)
Constant = CI * (T)

Now if T is decreased by 16.67 %

To keep the output of expression as constant we need to increase CI.

If we calculate then increase in CI is coming 20 %

Where I am wrong ???
@dream_IIMA said:
@Calvin4ever lik muje 40!/ 41 karna hai toh 40 remdr bt 38!/41 ??toh
Hey, that shud be easy too. Let's say 38! mod 41 is x. Now we already know, 40! mod 41 is 40.
So (x*39*40) mod 41 = 40 --> 2x=40 --> x=20 😃
@Cat.Aspirant123
@DeAdLy I think option 1 is the answer. Every criteria is satisfied including age.

1. Ralph knows that he is going to have to replace his roof soon. If he has the roof replaced now, it will cost $10,000. He could wait 5 years, but it will then cost him $20,000. At what rate will these options cost the same. (Hint: This is also known as the break-even point. )

2. Christine is a new homebuyer. She wants to make sure that she incorporates the cost of maintenance into her decision. She estimates that routine repairs and maintenance on the home she is considering will be $1,590 in the first year (one year from now). Due to the increasing age of the home, she expects that maintenance costs will increase 6% annually. The interest rate is 5%. If she plans to be in the home for 10 years, what is the present value of all future maintenance? (Note that maintenance costs will change annually, and starts one year from now and she plans to do the last one before selling her house.)
3. Rondo is in the market for a new car. He has narrowed his search down to 2 models. Model A costs $32,000 and Model B costs $28,000. With both cars he plans to pay cash and own them for 4 years before trading in for a new car. His research indicates that the trade in value for Model A after 4 years is 60% of the initial purchase price, while the trade in value for Model B is 45%. The interest rate is 5%. For simplicity assume that operating and maintenance costs for the models are identical. Which model is the better decision and how much "cheaper" is it than the alternative?
@Tyranitar said:
1.Ralph knows that he is going to have to replace his roof soon. If he has the roof replaced now, it will cost $10,000. He could wait 5 years, but it will then cost him $20,000. At what rate will these options cost the same. (Hint: This is also known as the break-even point. )

is ans 14.8??

after travelling 50km,a train is meeting with an accident and travels 3/4th of usual speed and reaches 45 min late .had the accident happened 10 km further on it would have reached 35 min late .find the usual speed??