Latest Elitmus Aptitude Question SOLUTION: Three men can do as much work as 5 boys and the wages of 3 boys are equal to those of 2 men. A work on which 40 boys and 15 men are employed takes 8 weeks and costs Rs 15750. How l

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(#M40033030) ELITMUS Numerical Ability question Time and Work Keep an EYE

Three men can do as much work as 5 boys and the wages of 3 boys are equal to those of 2 men. A work on which 40 boys and 15 men are employed takes 8 weeks and costs Rs 15750. How long would it take if 20 boys and 20 men were employed , and how much would it costs?

Asked In Elitmus Ankit Boae (10 years ago)

Unsolved Read Solution (13)

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Read Solution (13) :

Ankit Aggarwa;  (10 years ago)

around 69 days. Rs 12600

Is this solution Helpfull? Yes (15) | No (7)  

akshay kumar  (9 years ago)

3 men work = 5 boys work
so let work done by 1 boy in 1 day = 1/5;
then work done by 1 man in 1 day = 1/3;
so total work done in 8 weeks = work done by boys + work done by men
= 1/5*40*8*7 +1/3*15*8*7
=13*56;...........................................................................(i)
now let wage of 1 boy for 1 day = x;
wage of 1 man for 1 day =y;
so a/c quest,
3*x=2*y................................................(ii)
now
(8*7)(40*x+15*y)=15750.........................................(iii)
from (ii) and (iii)
x=(15750*2)/(56*125);
x=4.5;
y=6.75;

now... no. of dys taken by 20b and 20m to finish the work=z
z*(1/5*20+1/3*20) = 13*56;
z=(13*56*15)/20*8;
z=39*7/4;
z=9.75 week;
total amount....
20(4.5*9.75*7 + 6.75*9.75*7) .............(wage of boy=4.5; wage of men =6.75)
= 20(307.125 + 460.687)
= 15356.25.
so ans total time = 9.75 week and amount =15356.25.

Is this solution Helpfull? Yes (13) | No (1)  

Praveen kumar  (10 years ago)

for working:
3m=5b ==> 1m=(5/3)b
40b+15m=(8*7)=56 ==> 40b+15m=56
sub 1m=(5/3)b in 40b+15m=56
1b=56/65
sub 1b=56/65 in 40b+15m=56
1m=3640/3215
so (20*(56/65))+(20*(3640/3215))=40days

for wages:
3b=2m ==> 1b=2/3m
40b+15m=15750
sub 1b=2/3m in 40b+15m=15750
1m=378
1b=252
20*378+20*252=12600wages

Is this solution Helpfull? Yes (4) | No (10)  

Sagar Laxmikantrao Gomte  (10 years ago)

I think
68+(1/4)days & Rs. 19687.5

Is this solution Helpfull? Yes (4) | No (1)  

ganesh chemanchula  (10 years ago)

13621 rs..6 weeks approx

Is this solution Helpfull? Yes (2) | No (2)  

Himanshu gaur  (10 years ago)

If 65B can do in 56days then how it is possible that 1B will do in 56/65 days?

Is this solution Helpfull? Yes (1) | No (1)  

Ayush Barnawal  (7 years ago)

Check this out:
https://testbook.com/bank-clerk-practice/quantitative-aptitude/time-and-work-568a765c9b2dd258e7c25cbf/564b1252d0249b11db16e0d4

Is this solution Helpfull? Yes (1) | No   

swati  (7 years ago)

40boy+15men 1 day work=1/8
=>8boy+3men 1 day work=1/40
a/q 3men 1 day work=5 boy 1 day work
so 8boy+5boy 1 day work=1/40 (using above)
13boy 1 day work=1/40
1 boy 1 day work=1/40*13
so , 1 men 1 day work=1/8*3*13 (1men 1 day work=5*(1 boy 1 day work)/3)
so 20 men+20 boy 1 day work=4/39 (using above)
so total weeks taken=39/4=9.75weeks or 68.25 days (ans)
now,
a/q 3 boys 1 day wages=2men 1 day wages....(1)
let 2men 1 day wages=x=>so, 1 men1 day wages=x/2
so using (1)
1 boy wages=x/3
now, a/q
40*x/3*56+15*x/2*56=15750
x=(15750*6/56*125)=>13.5
so 1 men 1 day wages=x/2=>6.75
and 1 boy 1 day wages=x/3=>4.5
so, requird wages=(20*6.75*9.75*7)+(20*4.5*9.75*7)=15356.25(ans)

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sindhura  (10 years ago)

Anyone, please give us a complete and correct solution .
Thank You.

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Ranvir kumar  (9 years ago)

ur solution is ryt @akshay kumar.

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shubham pal  (8 years ago)

1 m=5/3 b...;(work relation between men and boys;)
40 b+15 m does a work in 56 days;
total work done by 40 b=40*56=2270(boys work a day);
total work done by 15 men=15*56=840(men day);
and 1 m= 5/3 b
therefore 840*5/3=1400 work done by boys in compare to men;
total work=2270+1400=3670;
now 20 b+ 20 m==??
1 m=5/3 b
20 b+20*5/3=160/3(boys)
and total work by boys is 3670;
therefore 3670*3/160=68.7 it is the total days the work will take to complete.
for wages it is same as Akshay .

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Madhu  (7 years ago)

6814days,Rs.15356.25

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Anuj kumar  (6 years ago)

Let the work of men be M and work of boys be B and their wages be wm and wb

Given 3 men can do as much work as 5 boys and wage of 2 men is equal to wage of 3 boys

∴ 3M = 5B

⇒ M = 5B/3

And 2wm = 3wb

⇒ wm = 3wb/2

40 boys and 15 men work for 8 weeks to complete a job and the work costs 15750

Total work done = 40B + 15M

⇒ Total work done = 40B + 15 × 5B/3

⇒ Total work done = 65B

Thus to complete 65B work 8 weeks are required

Total wage = 40wb + 15wm

⇒ Total wage = 40wb + 45wb/2 = 125wb/2

Given Total cost of work = 15750

Total cost = wage × number of weeks

15750 = 125wb/2 × 8

⇒ wb = 31.5

If 20 men and 20 boys work then

Total work = 20M + 20B

⇒ Total work = 20 × 5B/3 + 20B

⇒ Total work = 160B/3

To complete 65B work it took 8 weeks

∴ To complete 160B/3 time taken = 8160B3×65B

⇒ Time taken to complete 160B/3 work = 39/4 = 9 ¾ Weeks

Total wage = 20wm + 20wb

⇒ Total wage = 30wb + 20wb = 50wb

Total cost = wage × number of weeks

⇒ Total cost = 50 × 31.5 × 39/4

⇒ Total cost = 15356.25

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