One man and six women working together can do a job in 10 days.The same job is done by two men in 'p' days and by eight women in p+5 days. By what percentage is the efficiency of a man greater than that of a woman?

Options

1)

300%

2)

500%

3)

600%

4)

700%

Additional Notes: with detailed explanation,please do come up with shortcut also.

total number of factors are 144 ( 4*4*3*3=144) and factors that are divisible by 6 are 3*3*3*3 [ remove one 2 and one 3 from the factors given i.e 2*3*(2^2*3^2*5^2*7^2) ]

total number of factors are 144 ( 4*4*3*3=144) and factors that are divisible by 6 are 3*3*3*3 [ remove one 2 and one 3 from the factors given i.e 2*3*(2^2*3^2*5^2*7^2) ]

As per divisibility rule of 11, the number 77777777.....777 for 429 digits should leave a remainder 7 when divided by 11. Similarly, this number leaves a remainder of 10 when divided by 13 and a remainder 1 when divided by 8.

So the number is of the form: 11A+7 = 13B + 10 = 8C + 1.

First take 11A+7=13B+10...(i)

By Chinese remainder theorem, you get A = 5 and B = 4 (which give you 62 on both sides of the equation (i)). So the series of such numbers is given by 62+143D.

Now take 62+143D = 8C+1....(ii)

Again apply Chinese remainder theorem and you get C=97 and K=5 (giving you 777 on both sides of the equation (ii)). So the series of such numbers is given by 777+1144E. Hence remainder = 777. Option 3.

As per divisibility rule of 11, the number 77777777.....777 for 429 digits should leave a remainder 7 when divided by 11. Similarly, this number leaves a remainder of 10 when divided by 13 and a remainder 1 when divided by 8.

So the number is of the form: 11A+7 = 13B + 10 = 8C + 1.

First take 11A+7=13B+10...(i)

By Chinese remainder theorem, you get A = 5 and B = 4 (which give you 62 on both sides of the equation (i)). So the series of such numbers is given by 62+143D.

Now take 62+143D = 8C+1....(ii)

Again apply Chinese remainder theorem and you get C=97 and K=5 (giving you 777 on both sides of the equation (ii)). So the series of such numbers is given by 777+1144E. Hence remainder = 777. Option 3.

the equation can be reduced to : y= 15x/(5x-2)....... or y = 3+ 6/(5x-2) Now 5x-2 can take values as 1,2,3,6,-1,-2,-3,-4 this will only give inegral x as 0 or 1. But x can't be 0. So only 1 solution is possible.

Each 1*1 cube has 6 faces Total 1*1 cubes = 2*5*5 + 2*3*5 + 2*3*3 = 98 Total faces of small cubes = 98*6 = 588 Now, four sides of the 5*5 cube is painted So, total small cube faces painted = 4*5*5 = 100 Desired answer = 588-100 = 488

the equation can be reduced to : y= 15x/(5x-2)....... or y = 3+ 6/(5x-2) Now 5x-2 can take values as 1,2,3,6,-1,-2,-3,-4 this will only give inegral x as 0 or 1. But x can't be 0. So only 1 solution is possible. So, (x,y) = (1,5)

The job is done by 2 men in 'p' days and by 8 women in 'p+5' days... If the amount of work done by a man in one day is 'm' and that of a woman in 'w', We get p(2/m)=1 (p+5)(8/w)=1 Solving above two equations,we get m=2p and w=8p+40 =4m+40 Substituting the above values in 10(1/m+6/w)=1 {derived from first condition) we get a quadratic equation w^{2 }-140w+2400=0 Solving the equation will give you w= 120,20 For w=20 m gives a negative value so ruled out... Hence w=120 and m=20 Implies M can finish the work in 20 days and w in 120 days i.e., in one day m can do 1/20th of work and w can do 1/120th of work.So efficiency of m over w is [(1/20)-(1/120)]/(1/120)=500%

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