Three cylinders of height of 8 cm and diameters 0.24 m, 0.28 m and 0.16 m respectively are melted to form spherical solid balls of diameter 4 cm, then number of balls thus formed is
Nine men can finish a work in 20 days whereas 12 women can finish the same work in 18 days. If six men and nine women started working together. After 8 days 3 women left and 2 new men joined the work, The group continued working together till the end of the work. In how many days will they be able to do the remaining work ?
9 men can finish work in 20 days, so 1 man's 1 day work=1/(9x20)=1/180
12 women can finish work in 18 days, so 1 woman's 1 day work=1/(12x18)=1/216
6 men & 9 women's 8 days work=8x(6/180 + 9/216)=3/5
Remaining work=1 - 3/5=2/5
Given, after 8 days 3 women left and 2 new men joined, so in new group there are 8 men and 6 women
Now 8 men + 6 women's 1 day work=8*(1/180) + 6*(1/216) = 13/180
.'. Time required to complete remaining work = (2/5)/(13/180) = 72/13 days
Correct Option 5)
A pipe can fill a tank in 8 hours. After 3/5 of the tank is filled, four more pipes of half capacity are opened to fill the tank. What is the total time taken to completely fill the tank ?
Time taken by first pipe to fill the tank = 8 hours
.'. Time taken by first pipe to fill 3/5 of the tank = (3/5)/(1/8) = 24/5 hours
Remaining part of the tank to be filled = 1 - 3/5 = 2/5
Part of the tank filled by 1 existing pipe and 4 new pipes in 1 hour = 1/8 + 4x(1/16) = 3/8
Time taken by 5 pipes to fill remaining tank = (2/5)/(3/8) = 16/15 hours
.'. Total time taken = 24/5 + 16/15 = 88/15 hours = 5 hours 52 minutes.
Correct Option 6)
The average of some numbers is 57. If 68% of the numbers are increased by 6 and the remaining are decreased by 8, then the average so obtained will be:
Let there be total 'x' numbers, then new average = (57x + 0.68x*6 - 0.32x*8) / x = 58.52
Alternate Method:
Let there be 100 numbers and their average is 57, Sum=5700
For 68 numbers average=(57+6)=63, Sum=68*63=4284
For remaining 32 numbers average=(57-8)=49, Sum=32*49=1568
New average = (4284+1568)/100 = 58.52
Correct Option 5)
A train crosses a man running in opposite direction in 21 seconds and same train crosses a 240 meters long platform in 33 seconds. If speed of man is 15 km/hr, then speed of train is
Given, speed of man=15 km/hr=15*(5/18)=25/6 m/s
Let speed of train = x m/s
Relative speed of train w.r.t. man = (x + 25/6) m/s
Length of train = Time taken to cross man * Relative speed = 21*(x + 25/6)
Also, given train crosses 240 m platform in 33 sec
Length of (train+Platform) = Time taken to cross platform * Speed of train
21*(x + 25/6) + 240 = 33*x
21x + 175/2 + 240 = 33x
x = 655/24 m/s = (655/24)*(18/5) = 98.25 km/hr
Correct Option 8)
A and B undertook a work for Rs. 11,500. When they worked together A got Rs. 2,300 less than B and A takes 7 days more than B, when they work individually. In how many days A and B working together can do the whole work ?
Let A got Rs. x, then B Rs. (x+2300), then x + (x+2300)=11500
⇒ x=4600
Thus A got Rs. 4600 and B Rs. 6900 according to their share in work.
.'. Efficiency of A and B = 4600 : 6900 = 2 : 3
Ratio of number of days to complete the work by A and B = 1/2 : 1/3 = 3 : 2
Given, A takes 7 days more than B, so 3a - 2a=7 ⇒ a=7
Thus individually A takes 21 days and B takes 14 days
1 day's work of A and B = 1/21 + 1/14 = 5/42
Hence, A and B together can complete the work in 42/5 = 8⅖ days.
On 22/06/2022, Mr. Samay sets the clock right at 22:06 hrs. If the clock looses 6 seconds in every 22 minutes, what will be the exact time when clock shows 22:06 hrs next day ?
Given, clock looses 6 minutes in every 22 minutes.
⇒ When actual time is 22x60 sec=1320 sec, Clock shows (22x60-6) sec =1314 sec
Time between 22:06 hrs of today and tomorrow=24 hrs=24x3600 sec
.'. When clock shows 24x3600 sec, actual time=24x3600x(1320/1314)=86794.5205 sec
Now 86794.5205 sec=24 hrs 6 min 34 sec
⇒ Actual time is 6 min 34 sec ahead of 22:06 hrs i.e 22:12:34
Correct Option 4)
To celebrate International Yoga day, the students of Sanskriti School gathered in a ground where they are arranged in rows to perform Yogasanas. If 2 students are extra in a row, there would be 3 row less. If 4 students are less in a row, there would be 9 rows more. Find the number of students in a school.
Let the number of rows be x and number of students in a row be y.
Total students of the school= Number of rows * Number of students in a row = xy
Case 1:
Total number of students=(x−3)(y+2)
⇒ xy=(x−3)(y+2)
2x−3y = 6 -----(i)
Case 2:
Total number of students=(x+9)(y−4)
⇒ xy=(x+9)(y-4)
-4x+9y = 36 -----(ii)
Solving equations (i) & (ii), we get, x=27, y=16
.'. Total students = xy = 27*16 = 432
Correct Option 8)
School A has boys to girls in the ratio 5 : 6 and school B has girls to boys in the ratio 8:7. If the number of students in school A is at least twice as many as the number of students in school B, what is the minimum percentage of boys when both schools are considered together?
Let school A has Boys=5x, Girls=6x and school B has Boys=7y, Girls=8y
Given, number of students in school A is at least twice as many as the number of students in school B and we have to find minimum percentage of boys out of total students.
For the minimum percentage, we need to consider the other extreme-where school A has exactly twice as many students as school B.
⇒ (5x + 6x) = 2*(7y + 8y)
y=(11/30)*x
Now total boys=5x+7y=5x+7*(11/30)*x=(227/30)*x
Total students of school A & B = 11x+15y = 11x + 15*(11/30)*x = (33/2)*x
.'. Minimum percentage of boys = [(227/30)*x / (33/2)*x]*100 = 45.86%