Solve the following questions

1. Unit digit of 7^173?

2. Two train coming towards from distance 24 miles with speed 12 miles/hr, a fly randomly flying between two trains at the speed of 18 miles/hr.how many distance covered by the fly before will collide?

3. What is the increase of volume of a sphere if its radius increases by 10%?

4. A man climbing in a rock at 24 km/hr and downhill 36 km/hr. determine avg speed?

5. Problem on language (some percent known German, some knows French, some English)
Ans: 24

5. Here two same size glass one is filled 1/3 of milk and other is 1/4 milk. Then the glasses filled with water and mixed, what is the percentage of milk now?

6. One is filled 1/3 of milk and other is 1/4 milk. Then the glasses filled with water and mixed, what is the percentage of milk now?

7. If the time required for write one digit is one second then how many time for (10^10)^10?

8. In 1930 the age of one student is same as the last two digit of his year of birth and the case is same for his grandfather also, what is the sum of age his and his grandfather?
Ans: 80 check

9. Blue socks:4 pair, Red socks:3 pair, White socks:2 pair, how many socks one will take for two different socks.

10. What is the probability of 2 man will be born in a same month
Ans: 1/12, 1/6, 1/24, 1/2

11. There is a square ground of side 14 cm, two horses r there in two different point of the square such that they can just touch them, how much grass will not be covered by the horses.
Ans: 14*14-2*(1/4)*pi*(7*sqrt2)^2)

12. A man is started his journey from point A he goes 1000 km south then 1000 km east, 1000 km north, then 1000 km west. Where is he now.
Ans: (i)at point A ii) 1000 km east from A (iii) (iv)

• 7^173: for unit digit we xpress d nmbr as a nmbr having 1 in its unit place. so 7^173= (7^4)^43*7= (2401)^43*7=.....01*7=...07. So unit digit:7
• 10 years agoHelpfull: Yes(30) No(2)
• 4> Shortcut formula is
  Average speed= (2*upstream speed*downstream speed)/(upstream speed + downstream speed)
  So, ans will be (2*24*36)/(24+36)=28.8 miles/hr
• 10 years agoHelpfull: Yes(25) No(1)
• 2.train will meet after one hour.
  hence distance covered by the fly=18*[24/(12+12)]=18miles ans.
• 10 years agoHelpfull: Yes(20) No(4)
• 3. Let the radius of the sphere be r.
  
  ∴ Volume of the sphere 4/3*pi*r^3
  
  Now, the radius is increased by 10%.
  
  ∴ New radius of the sphere r+ 10/100*r=11/10r
  
  ∴ New volume of the sphere 4/3*pi*(11/10r)^3=4/3(1331/1000)*pi*r^3
  
  ∴ Percentage increase in volume= (4/3*pi*r^3(1331/1000-1))/(4/3*pi*r^3)*100
  =331/1000*100
  =33.1
  
  Thus, the percentage increase in the volume of the sphere is 33.1%.
  
• 10 years agoHelpfull: Yes(19) No(3)
• For 7^173, there is a thumb rule:
  7^1=7
  7^2=49
  7^3=343
  7^4=2401
  7^5=16807
  7^6=117649
  .....
  So,the series is oscillating after 4th power producing the same unit digit.
  Hence we have to divide the power 173/4 and the remainder is 1.
  so,7^1=7
  hence 7^173 produces unit digit 7.
  REMEMBER, in case of dividing a power by 4,no remainder means it's 4,not 0.
• 10 years agoHelpfull: Yes(17) No(0)
• 6) total milk =1/3 + 1/4 =7/12
  total water = 2/3 + 3/4 = 17/12
  total milk =1/3 + 1/4 =7/12
  total water = 2/3 + 3/4 = 17/12
  vol = 2
  so % of milk =(7/12/2)*100=175/6
  
  
• 10 years agoHelpfull: Yes(9) No(1)
• 1> 7^173= 7^(4*43+1)=7*7^(4*43)===== unit place== 7
  
  2> trains will take total 24/(12+12)hr= 1 hr to collide.. so bee will fly 18 mile.. ans..
  3>beffore increase , v1= 4/3pi.r^3.. after increase, v2= 4/3 pi. r^3(1+1/10)^3
  so , increase= {(1+1/10)^3 - 1)*100%= (11^3- 10^)*100%/10^=11.1% ans.
  
  4. avg speed= (24-36)/2 = -4== 4km/hr downhill.. (take positive as uphill)ans..
  
  5> let vol of glasses be x each. so milk= x/3 + x/4= 7x/12.. percentage= 7x*100/(12*2x)=29.16% ans.
  
  8> let boys birth= AAXX year. so age= 1930-AAXX= xx so , 30-XX= XX... similarly , for grand father , 30+(100- YY)= YY. so , (30-XX)+(130-YY)= xx+YY so , 2(xx+yy)= 160... so sum off age== XX+ YY= 80....!!!!!!
  
  10> dont consider the no off pairs. as in blue socks , all of 4 lefft leg socks r similar , and all off 4 right leg socks r similar.. so from blue socks , u can choose one sock in 2 ways. either right , or left.. and same thing for others... so u can choose different socks in such way-- BW + BR + RW = 2*2+ 2*2+ 2*2= 12 ways.. ans..
  
  11> 2 men can born in 12* 12 ways. if the born in same month, then they can born in 12 way.. so prob= 12/(12*12)== 1/12.. ans.
  
  12> diagonal= 14root2.. so length of each rope= 14*root2/2=7 root2. so
  area= 2* pi/4 (7root2)^2
  
  13> same point... point A...
  
  
• 10 years agoHelpfull: Yes(8) No(19)
• 7) 101 secs
  
• 10 years agoHelpfull: Yes(6) No(7)
• (1).7^173
  Unit digit
  7^1=7(unit digit)
  7^2=-9(unit digit)
  7^3=--3(unit digit)
  7^4=--1(unit digit)
  after each 4 cycle the value of unit digit is repeated
  so
  173%4=1
  then
  7^1=7
  
• 10 years agoHelpfull: Yes(5) No(0)
• answer to 9 is 9
• 10 years agoHelpfull: Yes(4) No(3)
• 4. its answer is 28.8 km/hr.The formula to calculate average speed is TOTAL DISTANCE/TOTAL TIME
  
  so let the distance from bottom to top be x.
  
  time taken to go up=x/24
  
  time taken to return back=x/36
  
  so average speed = total distance/toatl time=2x/((x/24)+(x/36))=28.8
• 10 years agoHelpfull: Yes(4) No(3)
• 11) 12/(12*12)=1/12
• 10 years agoHelpfull: Yes(3) No(2)
• 11.We know area of square=(1/2)*(diagonal)^2 .So diagonal=Root2*side.
  Now this side is diameter of rope.
  hence ropeLength=14Root2/2=7Root2.
  The horses can cover 1/4 th area of circle.So area remaining uncovered araeSquare-2*(1/4)Pie*(ropeLength)^2
  14*14-(1/2)Pie*(7root)^2
• 10 years agoHelpfull: Yes(1) No(3)
• 11 ans : r= 14/2 => uncovered area=14^2-2*pi*r*r/4= 119
  
• 9 years agoHelpfull: Yes(1) No(0)
• 1.(10-3)^173
  (2+1)^173
  1^173=1
  ans is 9
• 10 years agoHelpfull: Yes(0) No(14)
• question 5: 2/3*3/1=2
  3/4*4/1=3
  hence the ratio of milk in 1 glass=2:1
  2 glass=3:1
• 10 years agoHelpfull: Yes(0) No(5)
• Ans 1: unit digit is 7
  
  units digit of the number starts repeating after 4.. therefore 173/4 gives remainder 1 7^1=7.
• 10 years agoHelpfull: Yes(0) No(3)
• answer of 12=(1)at point A
  
• 10 years agoHelpfull: Yes(0) No(2)
• Aneek could you please explain the solutions of question no 4,5.I cant understand your solution....
• 10 years agoHelpfull: Yes(0) No(3)
• 12. man made a square and tus cane to the same point
• 10 years agoHelpfull: Yes(0) No(1)
• 7.let y=(10^10)^10
  take log both sides
  logy=log(10^10)^10
  den y=10 by log property.so ans. is 10 sec.
• 10 years agoHelpfull: Yes(0) No(4)
• 1)7^173=
  we guys know about unit digit of 7^4=1=a;
  if u divide 173 by 4 it gives u reminder as 7 and quotient as 43
  i.e (a^43)*7=7(here a=1 so 1*7=7)
  finally our answer is 7
• 9 years agoHelpfull: Yes(0) No(0)
• 6.first glass water=1-1/3=2/3,second glass water=1-1/4=3/4(taking glass 1)
  they are miked =2
  total milk=2-(2/3+3/4)=7/12
• 9 years agoHelpfull: Yes(0) No(1)