Question

2. Mr. A is a computer programmer. He is assigned
three jobs for which time allotted is in the ratio of
allotted for each job gets wasted. Thereafter, owing
5:4 : 2 (jobs are needed to be done individually).
But due to some technical snag, 10% of the time
to the lack of interest, he invests only 40%, 30%
and 20% of the hours of what was actually allotted
to do the three jobs individually. Find how much
percentage of the total time allotted is the time in-
vested by A.
2015450/​

Answer 1

Given:

• Three jobs were assigned to Mr.A.
• The time for the three jobs is allotted in the ratio of $5:4:2$.
• Due to technical snag, $10$% of the time allotted to each work gets wasted.
• Due to lack of interest, he invests only $40$%, $30$% and $20$% of the hours that was actually allotted in the works, respectively.

To find:

The percentages of timings invested by Mr.A, out of total time allotted.

To be recollected:

• Percentage of any number is the ratio of that number to 100.
• When no values are given in particular, then each term of the ratio can be expressed as the product of assumed highest common factor.

Step-wise Solution:

Step-1:

As per the given data, the ratio of the timing allotted is $5:4:2$.

Let the highest common factor be '$x$'.

By multiplying this highest common factor to each term in the ratio, then the ratio becomes $5x:4x:2x$.

Step-2:

As given, due to some technical snag, $10$% of the time allotted to each work is wasted.

Let the first work be denoted by '$W_1$'.

Let the second work be denoted by '$W_2$'.

Let the third work be denoted by '$W_3$'.

⇒$W_1:W_2:W_3=5x:4x:2x$

Now, after the technical snag, the remaining time from the actually allotted time is given by:

$W_1:W_2:W_3=(5x-((10/100)*5x)):(4x-((10/100)*4x)):(2x-((10/100)*2x))\\W_1:W_2:W_3 = (5x-(5x/10)):(4x-(4x/10)):(2x-(2x/10))\\W_1:W_2:W_3=(5x-0.5x):(4x-0.4x):(2x-0.2x)\\W_1:W_2:W_3=4.5x:3.6x:1.8x$

⇒The remaining times after the technical snag are in the ratio of:

$W_1:W_2:W_3=4.5x:3.6x:1.8x$

Step-3:

Also, given that, due to lack of interest, he invests only $40$%,$30$% and $20$% of original timings allotted to the works.

⇒ He wasted $60$%, $70$% and $80$% on the original times allotted to the works, respectively.

Now, the ratios of the remaining times is given by:

$W_1:W_2:W_3=(4.5x-((60/100)5x)):(3.6x-((70/100)4x)):(1.8x-((80/100)2x))\\W_1:W_2:W_3=(4.5x-(0.6*5x)):(3.6x-(0.7*4x)):(1.8x-(0.8*2x))\\W_1:W_2:W_3=(4.5x-3x):(3.6x-2.8x):(1.8x-1.6x)\\W_1:W_2:W_3=1.5x:0.8x:0.2x$

⇒ The final times he invested on the work are in the ratio of $1.5x:0.8x:0.2x$.

Step-4:

The percentages of the times he invested on the works separately are given by:

$W_1=(1.5x/5x)*100\\W_1=0.3*100\\W_1=30$

⇒ He invested $30$% of the given time in the first work.

Now,

$W_2=(0.8x/4x)*100\\W_2=0.2*100\\W_2=20$

⇒ He invested $20$% of the given time in second work.

$W_3=(0.2x/2x)*100\\W_3=0.1*100\\W_3=10$

⇒He invested $10$% of the given time in third work.

Final Answer:

The timings invested by Mr.A. in the given works are $30$%, $20$% and $10$% of the original timings given for those particular works, respectively.