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) Tap1 can fill = 20 min
∴ Tap1 can fill 1 min = 1/20
Tap2 can fill = 12 min
∴ Tap2 can fill in 1 min = 1/12 min
Now (Tap1 + Tap2) 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
M1 = 5 girl, D1 = 17
M2 = (35/3 + 11) girl, D2 =?
= 35+33/3
= 68/3 girl
We know
M1 D1 = M2 D2
Or, D2 = M1 D1/M2 = 5X17/(68/3)
= 5X17X3/68
Or, D2 = 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)
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