1440 men had sufficient food for 32 days. How many men may leave so that the same food be sufficient for 40 days when the ration is increased by 11/2 times?(hint:The 1st element is 1 and the 2nd is 3/2 in the ratio for ration.)

1440 men had sufficient food for 32 days. How many men may leave so that the same food be sufficient for 40 days when the ration is increased by 3/2 times?(hint:The 1st element is 1 and the 2nd is 3/2 in the ratio for ration.)

1440 men <=> 32 days

40 days, with the same amount of food would obviously mean that there should be less men. So, as days increase, men decrease, meaning that men shares an inverse relationship with food.

men \propto \frac{1}{food}

men = \frac{k}{food}

The k comes when you remove the proportionality sign. Solve for k using the values given in the first statement and then find men when you have food and k for the second part.

672

Days :Ration :Men
(down) 32 :(down arrow) 1 : 1440 (up arrow)
40 : 3/2 : X

X/1440 = 1/(3/2) * 32/40
X = 2/3 * 32/40 * 1440
X = 768
Remaining men = 1440 - 768
= 672 Men By Uzair hashmi 8th standard