CRE 4 - Payments

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).

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.

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).

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).

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 = $\frac{8}{30}$ = $\frac{4}{15}$

∴ Fraction of work done by A and B in 8 days = $\frac{1}{3}$ + $\frac{4}{15}$ = $\frac{9}{15}$

∴ Fraction of work done by C in 8 days = 1 - $\frac{9}{15}$ = $\frac{6}{15}$

∴ Payment recieved by C = $\frac{6}{15}$ × 36000 = Rs. 14,400

Hence, 14400