Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x meters,
and length of the second train = 17y meters.
$\therefore$ (27x + 17y)/(x+y) = 23
=> 27x + 17y = 23x + 23y
=> 4x = 6y
=> x/y = 3/2.
Let the average age of the team = x
=> Sum of ages of all 11 members/11 = x.
=> Sum of ages of all 11 members = 11x
Age of the captain = 26
Age of the wicket keeper = 26 + 3 = 29
Sum of the ages of 9 members of the team excluding captain and wicket keeper
=> 11x - 26 - 29 = 11x - 55.
Average age of 9 members of the team excluding captain and wicket keeper
=> (11x - 55)/9.
Given that,
=> (11x-55)/9 = (x-1).
=> 11x - 55 = 9x - 9.
=> 2x = 46.
=> x = 23.
L.C.M. of 6, 9, 15 and 18 is 90.
Let required number be 90x + 4, which is multiple of 7.
Least value of k for which (90x + 4) is divisible by 7 is k = 4.
Hence, the required number = (90 $\times$ 4) + 4 = 364.
Ratio of initial investments = 1/2: 1/3: 1/4 = 6: 4: 3
Let their initial investments be 6x, 2x and 3x respectively.
P: Q: R = (6x x 2 + 3x x 10): (4x x 12): (3x x 12)
= 42: 48: 36 = 7: 8: 6.
Qs share = Rs. 378 x 8/21
= Rs. 144.
Let the speed of the stream be x km/hr. Then,
Speed downstream = (15 + x) km/hr.,
Speed upstream = (15 - x) km/hr.
So we know from question that it took 4(1/2) hrs. to travel back to same point.
So,30/(15+x) - 30/(15-x) = 41/2.
=> 900/(225-$x^2$) = 9/2.
=> $9x^2$ = 225.
=> x = 5 km/hr.
Total number of balls = (8 + 7 + 6) = 21.
Let E= event that the ball drawn is neither red nor green= event that the ball drawn is blue.
n(E) = 7.
$\therefore$ P(E) = n(E)/n(S) = 7/21 = 1/3.
Let sum = Rs. x Then, S.I. = Rs. 4x/9
Let rate = R% and time = R years.
Then, [x $\times$ R $\times$ R / 100] = 4x / 9 or $R^2$ = 400/9 or R = 20/3 = 6 2/3
Rate = 6 2/3 % and Time = 6 2/3 yrs. = 6 yrs. 8 months.
Time taken by X to complete the work = 20 days
Time taken by Y to complete the work = 12 days
Work done by X in a day = 1/20
Work done by Y in a day = 1/12
Work done by X in 4 days = 4 $\times$ 1/20 = 1/5
Work remaining after 4 days = 1 - 1/5 = 4/5
Work done by X and Y together in 1 day = 1/20 + 1/12 = 2/15
X and Y together complete 2/15 work in 1 day
=> X and Y together complete the work in 15/2 days
=> X and Y together complete 4/5 work = 15/2 $\times$ 4/5 = 6 days
So the work is completed in (4 + 6) = 10 days.
CP of 20 dozen = Rs. (48 x 20) = Rs.960
CP of 8 dozen = Rs. (48 x 8) = Rs. 384.
CP of 12 dozen =Rs. (960 384) = Rs. 576
Total S.P = Rs. (110/100 x 384 +120/100 x 576) = Rs.1113.60
Profit % = (153.60/960 x 100) % =16%.
Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.
Sum of the present ages of wife and child = (20 x 2 + 5 x 2) years = 50 years.
Hence, Husbands present age = (90 - 50) years = 40 years.
Mphasis Logical Reasoning Test
Coding/Decoding:In a secret language 7 is coded as A, 5 is coded as R, 2 is coded as E, 1 is coded as T, 4 is coded as O, 6 is coded as M and 3 is coded as S. What does 3271 represents?
This is a simple question, just apply the alphabets to the code.
3 represents S, 2 - E, 7 - A, 1 - T.
Hence the code 3217 represents the word SEAT.
In a certain code, TRIPPLE is written as SQHOOKD. How is DISPOSE written in that code?
Each letter in the word is moved one step backward to obtain the corresponding letter of the code.
A cyclist goes 30 km to North and then turning to East he goes 40 km. Again he turns to his right and goes 20 km. After this he turns to his right and goes 40 km. How far is from his starting point?
Village Q is to the North of the village P. The village R is in the East of Village Q. The village S is to the left of the village P. In which direction is the village S with respect to village R?
Pointing to Varman, Madhav said, "I am the only son of one of the sons of his father." How is Varman related to Madhav?
Madhav is the only son of one of the sons of Varmans father ? Either Varman is the father or uncle of Madhav.
Since E is the brother of B. Therefore, A is the father of E
But D is the wife of E. Hence, D is the daughter-in-law of A.
Insurance Company X is considering issuing a new policy to cover services required by elderly people who suffer from diseases that afflict the elderly. Premiums for the policy must be low enough to attract customers; therefore, Company X is concerned that the income from the policies would not be sufficient to pay for the claims that would be made.
Which of the following strategies would be most likely to minimize Company Xs losses on the policies?The chairman and secretary of the housing society have requested society members to use water economically to help society save on water tax.
Assumptions:(I) Majority of members of society are likely to follow the request.
(II) It is desirable to reduce expenditure wherever possible.
Nothing about the response of society members can be deduced from the statement so I is not implicit.But II is implicit.
Water supply in wards A and B of the city will be affected by about 50% on Friday because repairing work of the main lines is to be carried out.
Conclusions:(I) The residents in these wards should economize on water on Friday.
(II) The residents in these wards should store some water on the previous day.
The food processing industry was touted to be a sunrise industry for India some years ago and, on the face of it, there was little reason to doubt that
Conclusions:(I) India has an advantage in food processing because of the varied agro-climatic conditions and availability of raw materials.
(II) Food processing is one of the basic industries which supports our lives.