# CRE 4 - Payments | Arithmetic - Time & Work

**CRE 4 - Payments | Arithmetic - Time & Work**

A and B can complete a work in 30 and 40 days respectively. They both work together and finish the work. They get a total of Rs. 7,000 to complete the work. What the A's share (in Rs.)

- A.
Rs. 3000

- B.
Rs. 4000

- C.
Rs. 3500

- D.
None of these

Answer: Option B

**Explanation** :

We know that the ratio of payment = ratio of work done.

⇒ $\frac{{\mathrm{P}}_{\mathrm{A}}}{{\mathrm{P}}_{\mathrm{B}}}$ = $\frac{{\mathrm{e}}_{\mathrm{A}}\times {\mathrm{t}}_{\mathrm{A}}}{{\mathrm{e}}_{\mathrm{B}}\times {\mathrm{t}}_{\mathrm{B}}}$

Since both A and B work together, they work for same number of days

∴ $\frac{{\mathrm{P}}_{\mathrm{A}}}{{\mathrm{P}}_{\mathrm{B}}}$ = $\frac{{\mathrm{e}}_{\mathrm{A}}}{{\mathrm{e}}_{\mathrm{B}}}$ = $\frac{{\mathrm{n}}_{\mathrm{B}}}{{\mathrm{n}}_{\mathrm{A}}}$ = $\frac{40}{30}$ = $\frac{4}{3}$

⇒ P_{A} = $\frac{4}{7}$× 7000 = Rs. 4000.

Hence, option (b).

Workspace:

**CRE 4 - Payments | Arithmetic - Time & Work**

A, B and C can complete a work in 30, 40 and 50 days respectively. They work together and finish the work. They get a total of Rs. 9400 to complete the work. What the C's share (in Rs.)

Answer: 2400

**Explanation** :

We know that the ratio of payment = ratio of work done.

⇒ P_{A} : P_{B} : P_{C} = e_{A} × t_{A} : e_{B} × t_{B} : e_{C} × t_{C}

Since all three of them work together, they work for same number of days

∴ P_{A} : P_{B} : P_{C} = e_{A} : e_{B} : e_{C} = $\frac{1}{30}:\frac{1}{40}:\frac{1}{50}$ = 20 : 15 : 12

⇒ P_{C} = 12/47 × 9400 = Rs. 2400.

Hence, 2400.

Workspace:

**CRE 4 - Payments | Arithmetic - Time & Work**

A can do a piece of work in 40 days. Along with B he finished the work in 24 days and together they got Rs. 1,000 for it. What was B's share?

- A.
Rs. 500

- B.
Rs. 600

- C.
Rs. 400

- D.
Rs. 300

Answer: Option C

**Explanation** :

A can complete the work alone in 40 days.

∴ Work done by A in 24 days = $\frac{24}{40}$ = $\frac{3}{5}$ ^{t h}

∴ Work done by B in 24 days = 1 - $\frac{3}{5}$ = $\frac{2}{5}$ ^{th}

⇒ Payment that B recieves will be 2/5^{th} of the total payment = $\frac{2}{5}$ × 1000 = Rs. 400

Hence, option (c).

Workspace:

**CRE 4 - Payments | Arithmetic - Time & Work**

A, B and C can complete a task in 32, 16 and 24 days respectively. They start working together but A leaves 4 days after the start of the work while B leaves 6 days before the works gets completed. Find B's share out of Rs. 3120?

- A.
Rs. 1170

- B.
Rs. 1950

- C.
Rs. 1550

- D.
Rs. 1520

- E.
None of these

Answer: Option A

**Explanation** :

Let the work to be done = LCM (32, 16, 24) = 96 units

∴ Efficiency of A = 96/32 = 3 units/day

Efficiency of B = 96/16 = 6 units/day

Efficiency of C = 96/24 = 4 units/day

Let the time taken to complete the entire work = x days.

A works for 4 days.

B works for (x - 6) days

C works for x days

Total work done = Work done by A in 4 days + Work done by B in (x - 6) days + Work done by C in x days.

⇒ 96 = 3 × 4 + 6 × (x - 6) + 4 × x

⇒ 96 = 12 + 6x - 36 + 4x

⇒ 120 = 10x

⇒ x = 12

∴ B worked for 12 - 6 = 6 days

⇒ Work done by B = 6 × 6 = 36 units

⇒ Fraction of work done by B = $\frac{36}{96}$ = $\frac{3}{8}$ units

⇒ Payment for B = $\frac{3}{8}$ × 3120 = 1170

Hence, option (a).

Workspace:

**CRE 4 - Payments | Arithmetic - Time & Work**

A and B can complete a piece of work in 24 and 30 days respectively. A and B, with the help of C completed the same piece of work in 8 days. If they together got paid Rs. 36,000 for the work, find C's share?

Answer: 19200

**Explanation** :

A alone can complete the work in 24 days.

∴ Fraction of work done by A in 8 days = $\frac{8}{24}$ = $\frac{1}{3}$

B alone can complete the work in 30 days.

∴ Fraction of work done by B in 8 days = $\frac{8}{30}$ = $\frac{2}{15}$

∴ Fraction of work done by A and B in 8 days = $\frac{1}{3}$ + $\frac{2}{15}$ = $\frac{7}{15}$

∴ Fraction of work done by C in 8 days = 1 - $\frac{7}{15}$ = $\frac{8}{15}$

∴ Payment recieved by C = $\frac{8}{15}$ × 36000 = Rs. 19,200

Hence, 19200

Workspace:

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