Let food stock will be exhausted in x days .
Given, m₁ = 120, D₁ = 45
M₂ = 120 + 30 = 150
and D₂ = ?
Then, using M₁D₁ = M₂D₂

Correct Option: D

Let food stock will be exhausted in x days .
Given, m₁ = 120, D₁ = 45
M₂ = 120 + 30 = 150
and D₂ = ?
Then, using M₁D₁ = M₂D₂
⇒ 120 x 45 = 150 x D₂
∴ D₂ = 120 x 45/120 = 36

Given, M₁ = 6, M₂ = 8 , T₁ = 16 h,
and T₂ = ?, W₁ = W₂ = 1
According to the formula.
M ₁T ₁W₂ = M₂T₂W ₁

Correct Option: C

Given, M₁ = 6, M₂ = 8 , T₁ = 16 h,
and T₂ = ?, W₁ = W₂ = 1
According to the formula.
M₁T₁W₂ = M₂T₂W₁
∴ 6 x 16 x 1 = 8 x T₂ x 1
∴ T₂ = 16 x 6/8 = 2 x 6 = 12 h

Given, M₁ = 10 D₁ = 8, M₂ = ? and D₂ = 1/2
From M₁D₁ = M₂D₂

Correct Option: D

Given, M₁ = 10 D₁ = 8, M₂ = ? and D₂ = 1/2
From M₁D₁ = M₂D₂
⇒ 10 x 8 = M₂ x 1/2
⇒ M₂ = 10 x 8 x 2
∴ M₂ = 160

12 men =18 women
⇒ 1 man = 18/12 women
⇒ 8 men = 18/12 x 8 = 12 women
Given m₁ = 18 M₂ = 12 +16 = 28,
D₁ , D₂ = ? and W₁ = W₂ = 1
According to the formula
M₁D₁W₂ = M₂D₂W₁

Correct Option: A

12 men =18 women
⇒ 1 man = 18/12 women
⇒ 8 men = 18/12 x 8 = 12 women
Given m₁ = 18 M₂ = 12 +16 = 28,
D₁ , D₂ = ? and W₁ = W₂ = 1
According to the formula
M₁D₁W₂ = M₂D₂W₁
⇒ 18 x14 x1= 28 x D₂ x1
∴ D₂ = (18 x 14)/28 = 9 days

Alen's one day's work =1/21
Border's one day's work = 1/42
Alen and Border's two days work(working alternatively) = (1/21) + (1/42) = 1/14

Correct Option: B

Alen's one day's work =1/21
Border's one day's work = 1/42
Alen and Border's two days work(working alternatively) = (1/21) + (1/42) = 1/14
So, Alen and Border do 1/14 work in 2 days
So, they complete the work in 14 x 2 = 28 days.