Mix Test - 8

Work done by X + Y in one day = 1/10
Work done b X alone in one day = 1/15
Work done by Y alone in one day = 1/10−1/15 = 1/30
∴ Y alone will finish the work in 30 day 

length = l  , breadth = w and height = h
Surface area of rectangular iron box = 2(l × b + b × h + h ×l)
S = 2(l × w + w × h + h + l)
S = 2(lw + wh + hl)
when dimensions are doubled,
New Length = 2l, breadth = 2w, height = 2h
The new surface area of the iron box = 2(l × b + b × h + h × l)
S = 2(2l × 2w + 2w × 2h + 2h × 2l)
S = 2(4lw + 4wh + hl)
S = 8(lw + wh + hl)
No. of times surface area will increase = new surface area/surface area of iron box

surface area will increase 4 times.

radius of cone = 8 m and height of cone = 24 m

volume of cylinde r= 3017.14 m³
The volume of air that occupies the tent = Volume of the cylindrical part + Volume of the conical part
Volume of air that occupies the tent = (3017.14 + 1609.14 ) m³ = 4626.28 m³
The volume of air that occupies the tent = 4626.28 m³

This is a case of direct proportion as with a decrease in the number of apples the cost will also decrease

In direct proportion, the value of constant is given by X/Y

12/144 = 5/a (where a is the cost of apples)

144 × 5 = 12 × a

720/12 = a

Rs 60 = a

As y varies directly as x. So in direct proportion, the value of constant is given by x/y

3a - 2b - ab - (a - b + ab) + 3ab + b - a
= 3a - a - a - 2b + b + b - ab - ab + 3ab
= 3a - 2a - 2b + 2b - 2ab + 3ab
= a + ab

The answer is Direct proportion as in direct proportion two quantities increase or decrease together to keep the ratio of corresponding value constant.

This is a case of direct proportion as with increase in scale in map the actual distance covered will also increase 

In direct proportion the value of constant is given by X/Y

1/40000000 = 4cm/a (where a is the actual distance covered)

40000000 × 4 cm = a

160000000cm = a

1600 km (1 km = 1000 m = 1000 × 100 cm = 100000 cm)