# Please help me solve these

Soln. a/b=c/d ...............................................(1)

squaring

a2/b2=c2/d2

adding 1 to both sides

(a2/b2)+1=(c2/d2)+1

(a2+b2)/b2=(c2+d2)/d2

(a2+b2)/(c2+d2)=b2/d2=(b/d)(b/d)

but b/d=a/c (from 1)

therefore

(a2+b2)/(c2+d2)=(b/d)(a/c)=ab/cd

Ans d

Q-6. a/b=c/d=k(let) i.e, a=bk,c=dk

Now a^2 +b^2 /c^2+d^2= b^2(1+k^2)/d^2(1+k^2)= b^2/d^2

=b/d.b/d=b/d.a/c=ab/cd

a = 1, b = 2 , c = 4

a : c = 1 : 4

a^2 : b^2 = 1 : 4

b^2 : c^2 = 1 : 4

(a^2 + b^2) : (b^2 + c^2) = 1 : 4

Given in question, a/b=b/c ----- (1)

now from (1) , a/c= b2/c2 ----- option (a)

again , b/c=a/b =>b2/c2=a2/b2= a/c ------ option (c)

Now from (1) , a=bk,b=ck, then a2+b2/b2+c2= a/c ----- option (b)

Hence ans - (d)

Given p=3q=4r --(1) , 2q=5s=12t -- (2)

Now combine both, we will get 2p=6q=8r=15s=36t

again it can be written in the form , p/180=q/60=r/45=s/20=t/10= k (say)

Now match with all options which is given in question , we will find only option (d) , where it can not be integer. explaination --P/8 will be integer, but s/r= 20k/45k= not integer .

Hence option (d). Any doubt contact me on manoj.nitt@gmail.com

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Total time = 500/V hr

Consumption of petrol/hr = 2/2500 x V^2

Total Consumption of petrol = 2/2500 x V^2 x 500/V = 2/5 x V

Exp = 60 x 500/V + 30 x 2/5 V

To minimize exp, diff of above should be zero

12 – 30,000 * 1/ V^2 = 0

=> V^2 = 30,000/12

=> V = 50 lt

And total exp = 600 + 600 = Rs. 1200

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