CRE 5 - Man Days (single group of people)

Total work = Men × Days

Since total work is same in both cases.

⇒ Work done by 10 men in 8 days = Work done by 8 men in 10 days.

∴ M₁ × D₁ = M₂ × D₂

⇒ 10 × 8 = 8 × x

⇒ x = (10 × 8)/8 = 10 days.

Hence, 10.

15 men can do a piece of work in 56 days.

∴ M₁ = 15, D₁ = 56 days

Let x be the number of men needed to do the same work in 7 days.

∴ M₂ = x, D₂ = 7 days

∵ Work done by 15 men in 56 days = Work done by x men in 7 days

∴ M₁ × D₁ = M₂ × D₂

∴ 15 × 56 = x × 7

∴ x = 120 men

Hence option (b).

When M₁ men can complete W₁ work in D₁ days while M₂ men can complete W₂ work in D₂ days, then

∴ $\frac{{\mathrm{M}}_1{\mathrm{D}}_1}{{\mathrm{W}}_1}$ = $\frac{{\mathrm{M}}_2{\mathrm{D}}_2}{{\mathrm{W}}_2}$

Now, 4 men can reap 80 hectares in 48 days, and 24 men reap 'x' hectares in 30 days.

⇒ $\frac{4\times 48}{80}$ = $\frac{24\times 30}{x}$

⇒ $\frac{4\times 48}{24\times 30}$ = $\frac{80}{x}$

⇒ x = 300

Hence, 300.

Let 8 men can cut 'x' number of trees in 24 days working 6 hours a day, while 3 men can cut '3x' number of trees in 48 days working 'h' hours per day.

∴ $\frac{{\mathrm{M}}_1{\mathrm{H}}_1{\mathrm{D}}_1}{{\mathrm{W}}_1}$ = $\frac{{\mathrm{M}}_2{\mathrm{H}}_2{\mathrm{D}}_2}{{\mathrm{W}}_2}$

⇒ $\frac{8\times 6\times 24}{x}$ = $\frac{3\times h\times 48}{3x}$

⇒ h = $\frac{8\times 6\times 24\times 3}{3\times 48}$ = 24

Hence, 24.

18 men in 10 hours make 168 wood chairs i.e. work done by 18 men in 10 hours is 168.

After 3 men leave, total number of men = 18 – 3 = 15

Let 15 men make x chairs in 8 hours.

$\frac{M_1{H}_1}{W_1}=\frac{M_2{H}_2}{W_2}$

∴ $\frac{18\times 10}{168}=\frac{15\times 8}{x}$

∴ x = 112 chairs

Hence, option (d).

Let the number of men initially be 'm'.

m men can complete the work in 20 days while (m - 10) men can complete the same work in 40 days.

∴ m × 20 = (m - 10) × 40

⇒ m = 2m - 20

⇒ m = 20

Hence, option (d) 

Work rate = 90 women 

Time = (18 × 9) hours

∴ Work done = (90 × 18 × 9) women hours

Later, work rate = 54 women

Time = (d × 6) hours  (d = number of days)

Since work done is the same,

∴ 90 × 9 × 18 = 54 × 6 × d 

d = 45 days

Hence, option (e).

Total food available for 900 patients for 60 days = 900 × 60 units

Total food consumed by 900 patients in 40 days = 900 × 40 units

Food remaining = 900 × 20 units

Number of patients remaining = 500

∴ Number of days = 18000/500 = 36

∴ Number of extra days = 36 – 20 = 16 days

Hence, option (d).

112 boys manufacture 128 toys in a day by working 8 hours

Let 42 boys manufacture 210 toys by working 5 hours a day, in x days

$\frac{M_1{D}_1{H}_1}{W_1}=\frac{M_2{D}_2{H}_2}{W_2}$

∴ $\frac{112\times 1\times 8}{128}$ = $\frac{42\times x\times 5}{210}$

∴ 112 × 1 × 8 × 210 = 42 × x × 5 × 128

∴ x = 7 days

Hence, option (c).

6 machines can produce 180 bottles per hour 

Hence, 1 machine can produce 180/6 = 30 bottles per hour and 15 bottles in 30 minutes.

∴ 15 machines can produce 15 × 15 = 225 bottles per hour.

Alternately,
$\frac{{\mathrm{M}}_1{\mathrm{H}}_1}{{\mathrm{W}}_1}$ = $\frac{{\mathrm{M}}_2{\mathrm{H}}_2}{{\mathrm{W}}_2}$

⇒ $\frac{6\times 60}{180}$ = $\frac{15\times 30}{B}$

⇒ B = $\frac{15\times 30\times 180}{6\times 60}$ = 225

Hence, option (a).

10 men working 6 hours a day can dig a well in 7 days.

Let x be required to dig a well in 4 days by working 14 hours a day.

$\frac{M_1{D}_1{H}_1}{W_1}=\frac{M_2{D}_2{H}_2}{W_2}$

∴ 10 × 7 × 12 = x × 4 × 14

∴ x = 15 men

Hence, option (a).

Total water available for 280 members for 180 days = 280 × 180 units

Total available consumed by 280 members in 100 days = 280 × 100 units

Water available after 100 days = 280(180 – 100) = 280 × 80 units

Number of members after 100 days = 320

∴ Number of days that the water will sufficient = 22400/320 = 70 days.

Hence, option (e).

Let the men required = x

We know that

Work = strength × time

∴ $\frac{m_1\times h_1\times t_1}{w_1}=\frac{m_2\times h_2\times t_2}{w_2}$

∵ Work ∝ wages

∴ $\frac{16\times 4\times 8}{80}=\frac{x\times 6\times 16}{120}$

⇒ x = 8 men

Hence, option (d).

The amount of food consumed by 400 soldiers in 100 days = 10 tonnes = 10 × 1000 = 10000 kg

The amount of food consumed by 400 soldiers in 20 days = (20 × 10000)/100 = 2000 kg 

The amount of food consumed by 40 soldiers in 20 days = 2000/10 = 200 kg

Hence, option (d).