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by Ketki T - Thursday, 3 September 2009, 04:04 PM

1] A horse can pull an empty cart at the speed of 18 kmph per hr & the reduction in its speed is directly proportional to the square root of the number of boxes it can carry of equal weight of 10 kg each. If the speed of the cart is 12 km per hr, when 9 boxes are loaded in the cart. Find the max weight that can be carried if the speed of the cart is to be maintained atleast 10 kmph

a] 16 kg
b] 160 kg
c] 100kg
d] 159 kg

2] 3 friends A,B & C started a firm by investing in the ratio of 2:3:4 respectively. A withdrew half of his money after some months. A few months before the end of the yr, C too withdrew 1/4 of his money. If they distributed their profits in the ratio 2:4:5 respectively, then after how many months did C withdrew 1/4th of his money ?

a] 6
b] 9
c] 4
d] cannot be determined

3] If m/n = p/q = a/b = 1/3 find the value of 2m^2+p^2+3a^2/ 2n^2+q^2+3b^2

a] 6
b] 9
c] 4
d] 1/9

4] Rajesh & suraj run around a circular track of 1000 m in circumference. Rajesh can run 50 m in 5 s & suraj can run a distance of 60 m in 5 s. What should be the head start given by the faster runner to the slower so that both the runners reach the finishing line at the same time?

a] 233.33 m

b] 200 m

c] 188.89 m

d] 166.67 m

5] X set out at 12 noon to walk from Borivali to Bandra & a friend of him Y started at 2 pm on the same day to walk from Bandra to Borivali by the same road. They met on the road  at 5 mins past 4 & both of them reach their destination at exactly the same time. At what time did they both reach their destination ?

a] 5pm
b] 6 pm
c] 7 pm
d] 8 pm

explain ur answers in detail


by Dipak Gondhali - Monday, 8 March 2010, 12:53 AM
  1) Let 'n' be no.of boxex then speed of cart is given by
speed=18-a*root(n) where a is const.
from given data speed=12 when n=9 ; we get a=2.
hence equation is speed=18-2*root(n)
thus for speed=10kmph we get n=16
hence total weight of cart=16*10=160 kg

squaring gigen eq. m^2/n^2=p^2/q^2=a^2/b^2=1/9

by slight modification    2m^2/2n^2=p^2/q^2=3a^2/3b^2=1/9
by using ratio pro. rule(ie. if a/b=c/d then a/b=a+c/b+d=c/d)
we get ans. as 1/9

by Ankit Chaudhary - Friday, 26 March 2010, 06:45 PM
  1 n 3 r replied...

rest ans are: 2 - b, 4 - d, 5 - c

Q 4 is straight frwrd....say Rajesh has a start of 'x' meters, so he has to cover '1000-x' m's. Both finish at the same time, hence:

(1000-x)/10 = 1000/12, solve now for 'x'...simple!

Q 2 is a simple logic based...

say 2x,3x,4x are initial investments

So after some months, A becomes 2x-x = x
and C becomes 4x-x = 3x, B remains the same.

So profit ratios which are 2:4:5 depend on the time for which the money was put by the investors.

So, we can say profits are 2y,4y,5y

Suppose B had points 12*3=36 points, he invested his money for all 12 months and had a ratio '3'.

Now profit is 2:4:5, so A must have 18 points, since we gave B 36!!
Simple thinking shows if A takes half the money after 6 months, then he has 6*2 + 6*1 = 18 points.

So, 2:4:5 and 18:36:?, ? will be 45 ;)

now simple trial and error....C takes out money after 9 mnths...hence his points become 9*4 + 3*3 = 45...hence is the answer.

Simple funda....profits will be in the ratio of the investments only smile

Q 5....its also simple....though a lil hectic calculation based!

aah cant write it all here...try it again...its a very old thread btw....u must have figured it out....if still u havent....mail me!!
by tamseel najmi - Monday, 17 May 2010, 12:01 PM
  hey can you make question 3 more explanatory as its difficult to understand in such a manner
by TG Team - Thursday, 5 May 2011, 11:44 AM
  Hi Tamseel Najmi smile

3] If m/n = p/q = a/b = 1/3 find the value of 2m^2+p^2+3a^2/ 2n^2+q^2+3b^2

a] 6
b] 9
c] 4
d] 1/9

Let n = 3m, q = 3p and b = 3a, so given fraction becomes:
(2m² + p² + 3a²)/(2n² + q² + 3b²) =
(2m² + p² + 3a²)/(18m² + 9p² + 27a²) = 1/9.

Hope this is clear. smile

Kamal Lohia