Question
Sat March 21, 2015 By: Tejvarun Pathak

How to solve the following two questions :-
1   If 12 men or 15 women can finish a piece of work in 66 days, how long will 24 men and 3 women take to finish the work? 

2.   70 patients in a hospital consume 1350 litres of milk in 30 days. At the same rate, how many patients will consume 1710 litres in 28 days

Expert Reply
Vimala Ramamurthy
Sun March 22, 2015
1. space W o r k space d o n e space b y space a space m a n space i n space o n e space d a y equals fraction numerator 1 over denominator 66 cross times 12 end fraction equals 1 over 792 W o r k space d o n e space b y space a space w o m a n space i n space o n e space d a y equals fraction numerator 1 over denominator 66 cross times 15 end fraction equals 1 over 990 W o r k space d o n e space b y space 24 space m e n space a n d space 3 space w o m e n space i n space o n e space d a y equals 24 over 792 plus 3 over 990 equals 1 over 33 plus 1 over 330 equals 1 over 30 T h e r e f o r e comma space t h e space n u m b e r space o f space d a y s space t o space c o m p l e t e space t h e space w o r k space f o r space 24 space m e n space a n d space 3 space w o m e n equals fraction numerator 1 over denominator begin display style 1 over 30 end style end fraction equals 30 space 2. 70 space p a t i e n t s space c o n s u m e space 1350 space l i t r e s space o f space m i l k space i n space 30 space d a y s. I n space 30 space d a y s space p a t i e n t s space c o n s u m e space 1350 space l i t r e s space o f space m i l k. I n space o n e space d a y space 70 space p a t i e n t s space c o n s u m e space equals 1350 over 30 equals 45 space l i t r e s space o f space m i l k. 70 space p a i t e n t s space c o n s u m e space 45 space l i t r e s space o f space m i l k. o n e space p a t i e n t space c o n s u m e s space 45 over 70 equals 9 over 14 space l i t r e s space o f space m i l k  A n d space 1710 space l i t r e s space s h o u l d space b e space c o n s u m e space i n space 28 space d a y s. S o space i n d a y comma space 1710 over 28 equals 61 space l i t r e s space s h o u l d space b e space c o n s u m e d. L e t space x space b e space t h e space n u m b e r space o f space p a t i e n t s. E a c h space p a t i e n t space c o n s u m e s space 9 over 14 space l i t r e s space o f space m i l k T h u s comma space space w e space h a v e comma space x cross times 9 over 14 equals 61 rightwards double arrow x equals fraction numerator 61 cross times 14 over denominator 9 end fraction equals 95 space T h u s comma space 95 space p a t i e n t s space w i l l space c o n s u m e space 1710 space l i t r e s space i n space 28 space d a y s
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