Question

Four enemies A, B, C and D gather together for
a picnic in a park with their wives. A's wife con-
sumes 5 times as many glasses of juice as A. B's
wife consumes 4 times as many glasses of juice
as B. C's wife consumes 3 times as many glasses
of juice as C and D's wife consumes 2 times as
many glasses of juice as D. In total, the wives of
the four enemies consume a total of 44 glasses
of juice. If A consumes at least 5 glasses of juice
while each of the other men have at least one
glass, find the least number of drinks that could
have been consumed by the 4 enemies together.

​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

• Four enemies A, B, C and D gather together for a picnic in a park with their wives.

• A's wife con- sumes 5 times as many glasses of juice as A.

• B's wife consumes 4 times as many glasses of juice as B.

• C's wife consumes 3 times as many glasses of juice as C

• D's wife consumes 2 times as many glasses of juice as D.

• In total, the wives of the four enemies consume a total of 44 glasses of juice.

• A consumes at least 5 glasses of juice while each of the other men have at least one glass.

Let assume that

• A consumes x glasses

• B consumes y glasses

• C consumes z glasses

• D consumes w glasses.

So, it implies that

• A's wife consumes a glasses

• B's wife consumes b glasses

• C's wife consumes c glasses

• D's wife consumes d glasses

According to given condition

$\boxed{ \tt{ \: a = 5x}} \\ \\ \boxed{ \tt{ \: b = 4y}} \\ \\ \boxed{ \tt{ \: c = 3z}} \\ \\ \boxed{ \tt{ \: d = 2w}}$

Further given that

$\red{\rm :\longmapsto\:a + b + c + d = 44 \: }$

• Now, A consumes at least 5 drinks and B, C, D consumes atleast 1 drink.

So, Following cases arises

Case :- 1 When A consumes 5 glasses, so following possibilities exist for the wifes

So,

• a = 25, b = 12, c = 3, d = 4

OR

• a = 25, b = 8, c = 9, d = 2

OR

• a = 25, b = 8, c = 3, d = 8

OR

• a = 25, b = 4, c = 3, d = 12

OR

• a = 25, b = 4, c = 9, d = 6

It means consumption of enemies is atleast 12

Case :- 2 When A consumes 6 glasses, so following possibilities exist.

So,

• a = 30, b = 4, c = 6, d = 4

It means consumption of enemies is 11

Case :- 3 When A consumes 7 glasses, so following possibilities exist

x = 7, y = 1, z = 1, w = 1

So,

a = 35, b = 4, c = 3, d = 2

It means consumption of enemies is 10.

Further no possible cases.

So, In case 3, the consumption is minimum.

Thus, 10 is the least number of drinks that could have been consumed by the 4 enemies together.