**ML Aggarwal CBSE Solutions Class 8 Math 8th Chapter Direct and Inverse Variation Exercise 8.3**

**(1) **Farmer can complete = 10 days

∴ Farmer 1 days work = 1/10

Farmer’s wife can complete = 8 days

∴ Farmer’s wife 1 days work = 1/8

∴ Both can days work = 1/10 + 1/8

= 8+10/80

= 18/80

= 9/40

∴ 11 can complete = 40/9 days

= 4 4/9 days.

**(2) **Let, total work = 1

∴ A can do 2 days = 1/5

∴ A can do 1 days = 1/5X2 = 1/10

B can do 1 days = 2/3

∴ B can do 1 days = 2/3X8 = 1/12

∴ (A+5) do 2 days = (1/10 + 1/12)

= 6+5/60

= 11/60

∴ (A+B) do complete the work = 60/11 = 5 5/11 days.

**(3) **Tap_{1} can fill = 20 min

∴ Tap_{1} can fill 1 min = 1/20

Tap_{2} can fill = 12 min

∴ Tap_{2} can fill in 1 min = 1/12 min

Now (Tap_{1} + Tap_{2}) can fill together

Within 1 min = (1/20 + 1/12)

= 3+5/60

= 8/60

∴ Both can fill the tank = 60/8 min

= 7 1/2 min (Ans)

**(4) **A can do = 6 days

∴ A’s 1 day’s work = 1/6

B can do = 8 days

∴ B’s 1 days work = 1/8

∴ (A + B) 1 day’s work = 1/6 + 1/8 = 4+3/24

= 7/24

∴ (A + B) 2 days work = 7/24 X2 = 7/12

Now, B left.

∴ Rest work = 1 – 7/12 = 12-7/12 = 5/12

∴ A can do the rest work = (5/12)/(1/6)

= 5/12 X 6

= 2 1/2 days (Ans)

**(5) **A can do = 40 days

A’s 1 day’s work = 1/40

∴ A’s 8 day’s work = 8/40 = 1/5

∴ Rest work = (1 – 1/5)

= 5-1/5

= 4/5

∴ Rest work finished by B = 16 days

∴ B done 16 days = 4/5 work

∴ B done 1 days = (4/5)/16

= 4/5 X 1/16

= 1/20

∴ (A + B) both’s 1 day work = 1/40 + 1/20

= 1+20/40

= 21/40

∴ Together they done the work = 40/21 days.

**(6) **A do = 10 day

A’s 1 days work = 1/10

B do = 15 days

∴ B’s 1 days work = 1/15

∴ (A+B) 1 days work = 1/10 + 1/15

= 3+2/30

= 5/30

= 1/6

Now, let (A+B) together worked for x day.

∴ (A+B) x day’s work = x/6

Remaining work = 1 – x/6 = 6-x/6

A do rest work 5 days

∴ A 1 days work = (6-x/6) ÷ 5

= 6-x/6X5 = 6-x/30

According to qne –

6-x/30 = 1/10

Or, 6-x = 3

Or, x = 6-3 = 3 days (Ans)

**(7) **3 women = 5 girl

∴ 1 women = 5/3 girl

∴ 7 women = 5X7/3 = 35/3 girl

M_{1} = 5 girl, D_{1} = 17

M_{2} = (35/3 + 11) girl, D_{2} =?

= 35+33/3

= 68/3 girl

We know

M_{1} D_{1} = M_{2} D_{2}

Or, D_{2} = M_{1} D_{1}/M_{2} = 5X17/(68/3)

= 5X17X3/68

Or, D_{2} = 15/4

= 3 3/4 days.

**(8) **(A+B+C) togethers 1 day work =

= (1/2 + 1/6 + 1/3)

= 3+1+2/6

= 6/6

= 1

∴ Working together they need 1 day (Ans)

∴ They should divide the money in the ratio = 1/2 : 1/6 : 1/3

∴ Common factor = 1

∴ A’s get money = 1/2 X960 = 480 /- (Ans)

B’s get money = 1/6 X960 = 162 /- (Ans)

C’s get money = 1/3 X960 = 320 /- (Ans)

**(9) **(A + B + C) can do work = 15 days

∴ (A + B + C) 1 days work = 1/15

B can do a work = 30 day

∴ B’s 1 day work = 1/30

C can do a work = 40 days

∴ C’s 1 day work = 1/40

∴ A’s 1 day work = 1/15 – (1/30 + 1/40)

= 1/15 – 7/120

= 8-7/120

= 1/120

∴ A can do a work = 120 days (Ans)

**(11) **Pipe can fill = 12 h

∴ Pipes 1 hr work = 1/12

waste pipes can fill = 16 hr.

∴ Waste pipes 1 hr work= 1/16

Waste pipes 1 hr’s work by mistake.

To empty = 1/12 – 1/16

= 3-2/40

= 1/48

∴ waste pipe take to empty 48 hr. (Ans)