DIRECTIONS for the questions 1 to 5: Solve the following question and mark the best possible option.
A boat takes a total time of twelve hours to travel 105 kms upstream and the same distance downstream. The speed of the boat in still water is six times of the speed of the current. What is the speed of the boat in still water? (In km/hr)?
12
30
18
24
36
Answer: Option C.
Let ‘x’ be the speed of Boat in still water, and ‘y’ be the speed of current.
Then, according to the question,
Speed of the boat in still water = 6 speed of current
x = 6y
Also given that ,
105/(x+y) +105/(x-y) =12
105/7y +105/5y =12
12y=36
y=3
Therefore, x= 6×3=18
Speed of the boat in still water= 18kmph
At 60% of its usual speed, a train of length L metres crosses platform 240 metres long in 15 seconds. At its usual speed, the train crosses a pole in 6 seconds. What is the value of L (in metres)?
440
425
220
480
240
Answer: Option D.
Let usual speed = S m/s.
According to the question,
60% of S= (L+240)/15
9S= L+240………… (i)
Also given that, S = L/6
L = 6S …. (ii)
From (i) & (ii)
9S= 6S+240
3S= 240
S=80 m/s
From (ii)
L= 6×80 =480 m
P, Q and R have a certain amount of money with themselves. Q has 50% more than what P has, and R has 1/3rd of what Q has. If P, Q and R together have Rs. 240 then how much money does P alone have? (in Rs.)
75
60
120
80
90
Answer: Option D.
Assume that P has 2x amount
Therefore, Q = 3x amount (50% more than P)
And R = 3x × 1/3 = x
Ratio of P : Q : R = 2x : 3x : x = 2 : 3 : 1
Thus, P alone have = (2/6) × 240 = Rs. 80
A and B both start a small business with an investment of Rs. 3500 and Rs. 5600 respectively. At the end of few months from the start of the business, A withdrew from the business completely. If the annual profit was divided between A and B in the respective ratio of 5 : 12, then after how many months from the start of the business, did A leave the business?
Eight
Nine
Ten
Five
Four
Answer: Option A.
Let A invested his money for ‘X’ months.
A : B
3500×X : 5600×12 35X : 672
As A and B have profit ratio as 5:12
Thus,35x/672 =5/12
X=8
Hence, A has invested money for 8 months
The difference between S.I and C.I on certain of money for 3 years at 10% per annum is Rs. 248. Find the sum?
2000
8000
1600
4000
None of these
Answer: Option B.
Let us consider sum of money is Rs. 1000.
S.I. = 1000*10*3/100 =300
C.I. = 1000(1+10/100)*(1+10/100)*(1+10/100)-1000 =331
Difference between SI and CI = 331 – 300 = 31
Rs. 31 is difference, when sum = Rs. 1000
Rs. 248 is Difference, then sum = 1000*248/31 =8000.
DIRECTIONS for the questions 6 to 8: Solve the following question and mark the best possible option.
X ≤ Y
X ≥ Y
X > Y
X < Y
X = Y or No relationship between X and Y
2x2 + 7x + 5 = 0
3y2 + 5y + 2 = 0
Answer: Option A.
I. 2x2 +7x+5 = 0
=> x = - 5/2, -1
II. 3y2+5y+2=0
=> y = -3/2, -1
Thus, X ≤ Y
2x2 -13x + 21 = 0
3y2 -14y + 15 = 0
Answer: Option B.
I. 2x2 -13x+21=0
=> x = 3, 7/2
II. 3y2-14y+15=0
=> y = 3, 5/3
Hence, X ≥ Y
2x2 - 13x + 18 = 0
y2 – 7y + 12 = 0
Answer: Option A.
I. 2x2 -13x+18=0
=> x = 9/2, 2
II. y2-7y+12=0
=> y = 4,3
Thus, no relationship between X and Y
A can do a piece of work in 20 days. He worked for 5days. After this B did the remaining work in 3 days. How many days A and B will together take to finish the whole work?
10 days
10/3 days
5/3 days
12 days
None of these
Answer: Option D.
A’s one day work = 1/20 ; A’s = five day work = 5/20 = 1/4 , Remaining work = 1- 1/4 =3/4 , B can do 3/4 of work in 3 days, B can do 1 work in 3*4/3=4 days, B’s one day work = 1/4 , A’s one day work = 1/20, (A+B)’s one day work 1/4 +1/20 = 5+1/20 = 6/20 =3/10 . So, A and B together can do the work in 10/3 days.
10. A and B can do a piece of work in 10 days, B and C in 12 days and C and A in 15 days. If B alone works for 15 days and then joined by A and C, in how many days will the work be finished?
20 days
15 days
16 days
18 days
12 days
Answer: Option D.
A + B)’s one day work = 1/10; (B + C)’s one day work =1/12 ;
(C+A)’s one day work = 1/15 . 2(A + B + C)’s one day work = 1/10 + 1/12 +1/15 = 6+5+4/60 = 15/60 = 1/4 ;
A + B + C one day work =1/8 ; B’s 1 day work = (A + B + C)’s 1 days work – (C + A)’s 1day work = 1/8 -1/15 7= 15-8/120 = 7/120; B’s 15 day work = 7/120 *15 = 7/8 Remaining work = 1-7/8 = 1/8.
This remaining is to be done by A + B + C , A + B + C does 1 work in 8 days. A + B + C does 1/8 of work in 8 *1/8 = 1 day.
Total time taken to finish the work = 15 + 1 = 16 days.