Time and Work-Basic test 1

Answer: Option B

Explanation

According to the formula, if a person can do a piece of work in x days, then the work he can do in one day is $\frac{1}{x}$.

Here,

Person A can complete an assignment in 50 days

So, in 1 day Person A can do $\frac{1}{50}$^th part of the assignment

Similarly Person B can complete an assignment in 76 days

So, in 1 day Person A can do $\frac{1}{76}$^th part of the assignment

Hence option B is correct

Answer: Option B

Explanation

According to the above given formula, If M₁ persons can do W₁ work in D₁ days working T₁ hours a day and M₂ persons can do W₂ work in D₂ days working T₂ hours a day then, M₁D₁T₁W₂= M₂D₂T₂W₁

M₁=10, T₁=12, M₂=24, T₂=16, W₁=20, W₂=32, D₁=12, D₂=?

$$\begin{gathered} 10\times 12\times 12\times 32= 24\times {\mathrm{D}}_2\times 16\times 20 \\ {\mathrm{D}}_2=\frac{10\times 12 \times 12\times 32}{24\times 16\times 20} =\frac{12}{2}=6 \mathrm{days} \end{gathered}$$

Hence, 24 writers cab write 32 books in 6 days working for 16 hours a day

Hence option B is correct

Answer: Option A

Explanation

According to the formula, If person P can do a work in x days and person Q can do the same work in y days then, one day work of P and Q together is $\frac{\mathrm{xy}}{x+y}$

so, $\frac{10\times 12}{10+12}=\frac{120}{22}=5\frac{5}{11}\mathrm{days}$

Hence, is both of them work together, work will be completed in $5\frac{5}{11}$days

Hence option A is correct

Answer: Option B

Explanation

According to the formula, If person P can do a work in x days and person Q can do the same work in y days then, one day work of P and Q together is $\frac{\mathrm{xy}}{x+y}$

so, $\frac{6\times 12}{6+12}=\frac{72}{18}=4 \mathrm{days}$

Hence, is both of them work together, work will be completed in 4 days

Hence option B is correct

Answer: Option C

Explanation

In the given problem in 1 day,

(A+B) can do $\frac{1}{72}$ part of work

(B+C) can do $\frac{1}{120}$ part of work

(C+A) can do $\frac{1}{90}$ part of work,

So, in one day, 2(A+B+C) can do,

$$\begin{gathered} 2(\mathrm{A}+\mathrm{B}+\mathrm{C})=\frac{1}{72}+\frac{1}{120}+\frac{1}{90} \\ \mathrm{A}+\mathrm{B}+\mathrm{C}=\frac{5+3+4}{360\times 2}=\frac{12}{360\times 2}=\frac{1}{60} \end{gathered}$$

1 day work of A=[1 day work of (A+B+C)]-[1 day work of (B+C)]

$\frac{1}{60}-\frac{1}{120}=\frac{2-1}{120}=\frac{1}{120}$

Hence, A alone can finish te work in 120 days

Hence option C is correct