ML Aggarwal CBSE Solutions Class 8 Math 8th Chapter Direct and Inverse Variation Exercise 8.2
(1) (i) Inverse variation
(ii) Inverse variation
(iv) Inverse variation
(2) (i) 90 X 10 = 900
60 X 15 = 900
45 X 20 = 900
30 X 30 = 900
20 X 45 = 900
∴ xy = 900
∵ xy is constant
∴ x ∝ 1/y
∴ In the following table all pair of variable are in inverse variation.
(ii) 75 X 10 = 750
45 X 30 = 1350
30 X 25 = 750
20 X 35 = 700
10 X 65 = 650
xy is not constant.
∴ x & y are not inverse.
(3) Given, v ∝ 1/p
Where, volume = v
Pressure = P
Temperature = T
∴ VP = T. [Where, T = constant]
Now, given data –
V1 = 630 cc, v2 = 720 cc
P1 = 360 mm, p2 =?
We know, V1 P1 = = v2 p2 = T
Or, v1 p1 = v2 p2
Or, 630 X 360 = 720 X p2
Or, P2 = 630X360/720
Or, p2 = 215 mm (Ans)
(6) Given, M1 = 12, D1 = 8 days
M2 =?, d2 = 6 days
∴ We know, M1 d1 = M2 d2
Or, M2 = M1 d1/d2 = 12X8/6
= 16 (Ans)
(7) No of taps = 8
Time = 27 min
Again no of tapes = 8 – 2 = 6
Let, x time to need
We know, x X 6 = 8 X 27
Or, x = 8X27/6 = 36 min (Ans)
(8) M1 = 560 person, D1 = 9 month
M2 =? D2 = 5 months.
We know, M2 X d2 = M1 X d1
Or, M2 X 5 = 9 X 560
Or, M2 = 9X560/5 = 1008
∴ Person required = 1008 – 560 = 448 (Ans)
(9) Let, no of x bottles would be filled.
∴ We know that,
x X 12 = 30 X 10
Or, x = 30X10/12
= 100/4
= 25
∴ 25 bottles would be field (Ans)
(10) Given, s1 = 5km/h, T1 = 24 min
S2 =?, T2 = 20 min
We know,
S2 T2 = S1 T1
Or, S2 X 20 = 5 X 24
Or, S2 = 5X24/20 = 6 km/hr (Ans)
(11) Firstly, total class time = 8X40 = 320 min.
Total school time = (20+20+320) min.
Let, class period time would be x.
Now, According to question –
20+20+320 = 40+40+x
Or, 360 = 80 + x
Or, 360 – 80 = x
Or, x = 280
∴ Each period time = 280/8 = 35 min (Ans)
(12) M1 = 80, D1 = 60 – 15 = 45
M2 = (80+20), d2 =?
∴ We know, M1 d1 = M2 d2
Or, d2 = M1 d1/M2 = 80X45/100 = 36 days
∴ D2 = 36 days (Ans)
(13) M1= 1200,
d1 = 28-4
= 24 days
Let, x soldiers are left.
∴ M2 = (1200 – k) d1 = 32 days
∴ We know, M1 d1 = M2 d2
Or, (1200X24) = (1200 – x) X 32
Or, 1200 – x = 1200X24/32 = 900
Or, 1200 – 900 = x
Or, x = 300
∴ 300 soldiers are left (Ans)