AP ICET 26th April 2019 Shift-2

Let A can finish a work in x days, B can finish the work in y days.

A and B can finish the work in one days$$=\dfrac{1}{24}$$

$$\dfrac{1}{2x}+\dfrac{1}{y}=\dfrac{1}{24}----------------(i)$$

A works twice as much as C.

Hence C can finish the work in $$=2x$$

Hence C can finish the work in one days $$=\dfrac{1}{2x}$$

B and C can finish the work$$=30days$$

Hence, B and C can finish the work in one days$$\dfrac{1}{y}+\dfrac{1}{2x}=\dfrac{1}{30}-----------(ii)$$

From the equation (i) and (ii)

$$\Rightarrow \dfrac{1}{24}-\dfrac{1}{x}+\dfrac{1}{2x}=\dfrac{1}{30}$$

$$\Rightarrow \dfrac{1}{24}-\dfrac{1}{2x}=\dfrac{1}{30}$$

$$\Rightarrow \dfrac{1}{2x}=\dfrac{1}{24}-\dfrac{1}{30}$$

$$\Rightarrow \dfrac{1}{2x}=\dfrac{5-4}{120}=\dfrac{1}{120}$$

$$\Rightarrow x=60$$days

Hence, $$\dfrac{1}{y}=\dfrac{1}{24}-\dfrac{1}{60}=\dfrac{5-2}{120}=\dfrac{3}{120}$$

$$\Rightarrow y=40$$days.

As per the question,

The area of the trapezium is $$\frac{1}{2}(a^2 - b^2)$$ sq. units.

We know that, the area of the  trapezium$$=\dfrac{(a+b)(d)}{2}$$

Hence,

$$\Rightarrow \dfrac{(a+b)(d)}{2}=\frac{1}{2}(a^2 - b^2)$$

$$\Rightarrow d=\dfrac{2(a^2-b^2)}{2(a+b)}$$

$$\Rightarrow d=\dfrac{(a+b)(a-b)}{(a+b)}=(a-b)$$

Hence the distance between the parallel sides $$d=(a-b)$$

As per the condition given in the question,

Length of the field (l)$$=3\times $$breadth (b)

The side length of the square$$=12m$$

The area of the field $$=12\times$$ area of the pond

Area of the pond $$=12\times 12=144m^2$$

Hence, area of the field $$b\times 3b=12\times 144$$

$$\Rightarrow b^2=4\times 144$$

$$\Rightarrow b=2\times 12=24m$$

Hence, the length of the field $$=24\times 3=72m$$

As per the given question,

Area of the parallelogram$$=243cm^2$$

Let the length of the base$$=a$$

Length of the altitude $$=\dfrac{a}{3}$$

Hence, $$\dfrac{a\times a}{3}=243$$

$$a^2=243\times 3$$

$$a=7\sqrt{21}$$

As per the given question,

We joining two cube, which formed an cuboid.

Hence new length of the cuboid $$=7+7=14cm$$

Breadth of cuboid$$=7cm$$

And height of the cuboid$$=7cm$$

Hence, the total surface area of the cuboid $$=2(l\times b+b\times h+h\times l)$$

$$\Rightarrow 2(7\times 14+7\times 7+7\times 14)=2(98+49+98)=490$$

$$\Rightarrow =490m^2$$