official quant thread for cat08

[shivam_01]

Originally Posted by selebratinglife

Problem from today's AIMCAT:
Ganesh and sarath walk up an escalator which moves up with a constant speed. For every two steps that ganesh takes, sarath takes one step. Ganesh gets to the top of the escalator after having taken 30 steps, while sarath takes only 20 steps to reach the top.If the escalator were turned off, how many steps should each o them take to reach the top?

N=60 steps
using N-2x=20
and N-3/2x=30 we get N=60

taking refrence of

--------------------------------------------------------
Solution to Quantitative Question # 048
--------------------------------------------------------
Katrina walks down an up-escalator and counts 150 steps. Priyanka walks up the same escalator and counts 75 steps. Katrina takes three times as many steps in a given time as Priyanka. How many steps are visible on the escalator?

(a) 105 (b) 150 (c) 135 (d) 120 (e) none of these

Solution:
Let T be time Katrina takes to make 25 steps. Then Katrina takes 3T to make 75, and Priyanka takes 2T to make 150. Suppose the escalator has N steps visible and moves n steps in time T. Then Priyanka covers N + 2n = 150, N - 3n = 75. Hence N = 120, n = 15
=> Choice (4) is the right answer

[implex]

Originally Posted by shivam_01

N=60 steps
using N-2x=20
and N-3/2x=30 we get N=60

taking refrence of

Man!! Time lifted the problem from QQAD !! Goody goody !

[getintoiimb]

puys pls help me with these qns

1)ranjeet makes a deposit of Rs 50000 in PNB for a period of 2.5 yrs.if the rate of interest is 12 % per annum compounded half yearly find the maturity value of the money deposited by him?

ans : 66911.27

2)if a certain sum of money becomes double at SI in 12 yrs what would be the rate of interest per annum?

ans : 8(1/3)

3)a part of Rs 38800 is lent out at 6% per six months.thye rest of the amount is lent out at 5% per assum after 1 yr.the ratio of interest after 3 yrs frmo the time when the first amount was lent out is 5:4.find the second part that was lent out at 5%?

ans : Rs 28800

4)a sum fo Rs 1000 after 3 yrs at CI becomes a certain amount that is equal to the amount that is the result of a 3 yr depreciation from Rs 1728.find the difference between the rates of CI and depreciation(given CI is 10% p.a)

ans :2 %

5)the difference between CI and SI on a certain sum of money at 10% per annum for 3 yrs is Rs 620.find the principal if it is known that the interest is compounded anually?

ans :Rs 20000

6)an amount of Rs 12820 due 3 yrs hence is fully repaid in 3 annual installments starting after 1 yr.the first installment is 1/2 the second installment and the 2nd installment is 2/3 rd of the third installment.if the rate of interest is 10% per annum.find the 1st installment?

ans : Rs 2000

[shivam_01]

Originally Posted by getintoiimb

puys pls help me with these qns

1)ranjeet makes a deposit of Rs 50000 in PNB for a period of 2.5 yrs.if the rate of interest is 12 % per annum compounded half yearly find the maturity value of the money deposited by him?

ans : 66911.27

2)if a certain sum of money becomes double at SI in 12 yrs what would be the rate of interest per annum?

ans : 8(1/3)

3)a part of Rs 38800 is lent out at 6% per six months.the rest of the amount is lent out at 5% per assum after 1 yr.the ratio of interest after 3 yrs frmo the time when the first amount was lent out is 5:4.find the second part that was lent out at 5%?

ans : Rs 28800

4)a sum fo Rs 1000 after 3 yrs at CI becomes a certain amount that is equal to the amount that is the result of a 3 yr depreciation from Rs 1728.find the difference between the rates of CI and depreciation(given CI is 10% p.a)

ans :2 %

5)the difference between CI and SI on a certain sum of money at 10% per annum for 3 yrs is Rs 620.find the principal if it is known that the interest is compounded anually?

ans :Rs 20000

6)an amount of Rs 12820 due 3 yrs hence is fully repaid in 3 annual installments starting after 1 yr.the first installment is 1/2 the second installment and the 2nd installment is 2/3 rd of the third installment.if the rate of interest is 10% per annum.find the 1st installment?

ans : Rs 2000

@getintoiimb u have changed ur ming great man @getintoiima

my solution :

1)taking A=P(1+r/100)^n and since the compounded half yearly is said then it will be rate becomes half and time doubles
so we have
A=50000(1.06)^5
which gives 66911.27

2)Using S.I = P*R*T/100
and S.I = A-P we get
R=8(1/3)%

3)Using S.I = P*R*T/100
and taking the amount as x and 38800-x respectively we get
((x*6*6)/(12*100))/(((38800-x)*1*5)/100)=5/4

solving this we get answer as 28800.

4) A=P(1+r/100)^n
we get 1000(1+10/100)^3=1728(1-r/100)^3
using this we get the r as 8.333%

so the difference is 10-8.33% ~ 2% (check)

5)A=P(1+r/100)^n and C.I = P((1+r/100)^n-1)
we get the relation as
P((1+10/100)^3-1-30/100)=620 solving this we get P=20000

6)let the installments be (1/3)x , (2/3)x and x respectively hence the number and using the relation of S.I we get the answer x=6000 and hence the first installment is 2000.

hope i am clear

[selebratinglife]

Originally Posted by implex

(2,3) also satisfies. I am lookign for a solid approach ! something rigorous !

hmm..Really not able to find one..Only way that seemed out was taking 'a' as a constant and tried with different 'b''s and also tried with 'b' as a constant..Any specific method you're looking for?

[selebratinglife]

Easy one!
Let R1 and R2 respectively denote the maximum and the minimum possible remainders when (276)^n is divided by 91, for any natural number n, n>144. Find R!+R2

[amitkrsingh]

Originally Posted by selebratinglife

Easy one!
Let R1 and R2 respectively denote the maximum and the minimum possible remainders when (276)^n is divided by 91, for any natural number n, n>144. Find R!+R2

E(91)= 91(1-1/13)(1-1/7)= 72

So, if n is of the form 72m the remainder is 1. However remainder cant be 0 as 276%91= 3

For n=72m+1, 72m+2,72m+3,72m+4 Remiander will 3,9,27 and 81 respectively.

For n = 72m+5 remainder is 61
For n= 72m+6 remainder is 1

After this the cycle continues so R1+R2 = 81+1=82.

[harneet9]

Good question -
australia scored a total of x runs in 50 overs . india tied the score in 20% less overs . If India's average run rate had been 33.33% higher the scores would have been tied 10 overs earlier . Find how many runs were scored by austalia ?
a) 250
b) 240
c) 200
d) 175
e) none of above

[selebratinglife]

Originally Posted by harneet9

Good question -
australia scored a total of x runs in 50 overs . india tied the score in 20% less overs . If India's average run rate had been 33.33% higher the scores would have been tied 10 overs earlier . Find how many runs were scored by austalia ?
a) 250
b) 240
c) 200
d) 175
e) none of above

Answer can be any number..
50x=40y(x and y are respective run rates of australia and india)
Now even using the 2nd statement we get the same equation 30(4y/3) = 50x..No conclusion can be arrived at..

[srikar2097]

Originally Posted by harneet9

Good question -
australia scored a total of x runs in 50 overs . india tied the score in 20% less overs . If India's average run rate had been 33.33% higher the scores would have been tied 10 overs earlier . Find how many runs were scored by austalia ?
a) 250
b) 240
c) 200
d) 175
e) none of above

Initially,
aust. played 50 overs and scores x runs.
India played 40 overs and scores x runs.

Later,
avg. run rate inc. by 33.33% by india
=> x *4 * 100/40 * 3.
this is the runs scored per over. Total score is x, and at the above rate it reaches x in 30 overs.
=> [x *4 * 100/40 * 3] * 30 = x

x cancels out on both sides! Have I done something wrong here? I guess we cannot find out the score with this info...