Relationship between three numbers of a set is as follows:
(First Number+Second Number)/3 = Third Number
(30+54)/3=28
.'. Only correct set is (36, 45, 27), where (36+45)/3=27
Option 7)
A motorboat whose speed is 27 km/h in still water takes 20 minutes more to go 40 km upstream than to cover the same distance downstream. If the speed of the boat in still water is increased by 3 km/h, then how much time will it take to go 44 km downstream and 54 km upstream ?
Let speed of the stream=x km/h, then Downstream speed=(27+x) km/h and Upstream speed=(27-x) km/h
Difference of time for 40 km upstream & downstream = 40/(27-x) - 40/(27+x) = 1/3 hrs.
â‡’ xÂ² + 240x - 729 = 0
(x+243) (x-3) = 0
x=3 km/h
Now, new speed of a boat in still water=27+3=30 km/h
.'. Downstream speed=(30+3)=33 km/h, Upstream speed=(30-3)=27 km/h
Hence, time required for 44 km downstream and 54 km upstream = (44/33) + (54/27) hrs = 10/3 hrs = 3 hrs 20 min.
Correct Option 8)
Ratio of milk and water is 5:3. When 4.8 liters of mixture is taken out and added 800 ml milk and 600 ml water, the difference of milk and water in a mixture is 5 liters, then difference of quantities of water and milk in initial mixture was
Let in initial mixture, Milk=5x, Water=3x
Qty. of milk after taking out 4.8 liters of mixture and adding 800 ml milk=5x - (4.8*5/8) + 0.8 L = (5x - 2.2) L
Qty. of water after taking out 4.8 liters of mixture and adding 600 ml water=3x - (4.8*3/8) + 0.6 L = (3x - 1.2) L
Difference of milk and water = (5x-2.2) - (3x-1.2) = 5
2x - 1 = 5
x = 3
Difference of milk and water in initial mixture = 5x - 3x = 2x = 2*3 = 6 liters
Correct Option 2)
If cost of constructing a path of uniform width around a circular garden of diameter 50 meter at the rate of Rs. 350 per meter sq. is Rs. 144375, then width of a path is:
OPtion
1) 350 cm
2) 225 cm
3) 300 cm
4) 275 cm
5) 260 cm
6) 325 cm
7) 250 cm
8) 370 cm
9) 200 cm
10) None of these
Solution
Radius of garden r = 50/2 = 25 m.
Let the width of a circular path=x m, then outer radius=(25+x) m.
Area of a path = Total Cost/Rate per m. sq. = 144375/350 = 412.5 m. sq.
Also, Area of a path = Area of a outer circle - Area of inner circle = Ï€[(25+x)Â² - 25Â²]
â‡’ Ï€[(25+x)Â² - 25Â²] = 412.5
(22/7)*[625 + 50x + xÂ² - 625] = 412.5
4xÂ² + 200x - 525 = 0
4xÂ² + 210x - 10x - 525 = 0
(2x-5) (2x+105) = 0
â‡’ x=5/2, -52.5
Considering +ve value, x=5/2 or 2.5 m=250 cm
Correct Option 7)
A bag contains 5 green, 7 red and 4 white balls. If three balls are drawn one after the other with replacement, then the probability of getting balls of same colour is:
Total number of balls in a bag = 5+7+4 = 16
As the balls are drawn with replacement, so probability of drawing same colour ball each time will be same.
P(Drawing 3 Green balls) = (5/16)*(5/16)*(5/16) = 125/4096
P(Drawing 3 Red balls) = (7/16)*(7/16)*(7/16) = 343/4096
P(Drawing 3 White balls) = (4/16)*(4/16)*(4/16) = 64/4096
.'. Probability of getting balls of same colour = P(3 Green) + P(3 Red) + P(3 White) = 125/4096 + 343/4096 + 64/4096 = 532/4096 = 133/1024
Correct Option 9)
A number consists of four different digits where last digit is two times the first digit, second digit is two times the last digit and third digit at tens place is 3 less than the second digit. The difference of this four digit number and number formed by reversing its digit is:
Given, last digit is 2 times the first digit, so number can be: 1 __ __ 2 ; 2 __ __ 4 ; 3 __ __ 6 ; 4 __ __ 8
Also second digit is 2 times the last digit so we can have only two numbers from above four as other two will result into double digit at 2nd place .
.'. Remaining numbers are 1 4 __ 2 ; 2 8 __ 4
It is given that 3rd digit is 3 less than the 2nd digit, therefore, so we have numbers 1 4 1 2 and 2 8 5 4
As it is given that all four digits are different, so 1412 can not be the number and hence required number is 2854
Therefore difference of number and number formed by reversing digits = 4582 - 2854 = 1728
Correct Option 2)
Roshan's present age is five times his daughter's present age and five-eighth of his mother's present age. The average age of all of them is 32 years 8 months, then what is the difference between present ages of Roshan's daughter and mother (in years)?
Let Roshan's present age = x years
His daughter's age = x/5
His mother's age = (8/5)*x
Average of all three = [x + x/5 + (8/5)*x] / 3 = 98/3
14x / 5 = 98
x = 35
Present age of daughter=35/5=7 years
Present age of mother=(8/5)*35=56 years
Hence, required difference=56-7=49 years.
Correct Option 8)
A bus takes 1 hour 20 minutes more to travel a distance of 210 km, if its speed is reduced by 10 km/hr than actual speed, then find the time taken to cover a distance of 300 km at double the usual speed.
Let the usual speed of a bus=x km/h
Then, 210/(x-10) - 210/x = 4/3
xÂ² - 10x - 1575 = 0
(x-45) (x+35) = 0
x=45
.'. Time taken to cover 300 km at 90 km/h = 300/90 hrs = 3â…“ hrs = 3 hrs 20 min.
Correct Option 6)
Two varieties of tea having cost per kg Rs. 36 and Rs. 45 respectively are mixed in the ratio 13:8. How much quantity of this mixture should be sold at Rs. 45 per kg to get profit of Rs. 1950 ?
OPtion
1) 530 kg
2) 420 kg
3) 350 kg
4) 560 kg
5) 280 kg
6) 450 kg
7) 210 kg
8) 360 kg
9) 410 kg
10) None of these
Solution
For (13+8)=21 kg mixture, CP=36*13 + 45*8=Rs. 828
CP per kg=828/21=Rs. 276/7
Profit per kg = SP - CP = 45 - (276/7) = 39/7
â‡’ For profit of Rs. 39/7, quantity to be sold = 1 kg
.'. For profit of Rs. 1950, quantity to be sold = 350 kg.
Correct Option 3)
In an examination, 85% of the candidates passed in English and 65% of the candidates passed in Mathematics, but 5% failed in both of these subjects. If 154 candidates passed in both the subjects, the number of candidates who appeared in an examination was:
Given, 5% failed in both the subjects, so candidates passed in at least one subject=95%
Let total candidates=x, then 85% of x + 65% of x - 154 = 95% of x
0.85x + 0.65x - 154 = 0.95x
0.55x = 154
x = 280
Correct Option 8)
It is impossible to be a mathematician without being a poet in soul.
Sofia Kovalevskaya
As a toddler when I looked at my fingers and wondered,
you helped me to count numbers.
As a kid when I looked at stars with awe,
you helped me and told that's infinity.
As a teen when my confused mind often went blank,
you told that's zero and eventually