# Please help me solve these

Hi Please help me solve the questions mentioned below. Kindly mention the steps in solving and not the answer alone.

1. If (bx-ay)/b=(cy-bz)/c=(az-cx)/a and given that bx is not equal to ay, cy not equal to bz and az not equal to cx, which of the following is true

a)a+b=c b)a+b+c=0 c)ab+bc+ca=0 d)ab+bc-ca=0

ans given: c

2. The consumption of petrol per hour of my car varies directly as the square of its speed. When the car is travelling at 50kmph its consumption is 2ltrs. If each litre costs Rs.30 and other expenses per hour is Rs 60, then what would be the minimum expenditure required to cover a distance of 500km?

a) Rs 800 b) Rs 1200 c) Rs 1500 d)Cannot be determined

Ans given: Rs 1200

3. If a,b and c are in continued proportion, then which of the following is equal to a : c?

a) a^{2} : b^{2} b) (a^{2}+b^{2}) : (b^{2}+c^{2}) c)b^{2} : c^{2} d)All of these

Ans given: d

4. A writer gets a fixed amount for his book apart from the royalty that he gets per book sold. He gets Rs. 30000 and Rs. 50000 for 1000 and 2000 books sold respectively. What is his income per book, if 5000 books are sold

a) Rs 17 b)Rs 20 c)Rs 21 d)Rs 22

Ans given: d

5. P, Q, R, S and T are five integers satisfying P=3Q=4R and 2Q=5S=12T. Which of the following pairs contain a number that can never be an integer?

a) (2P/15, Q/T) b) (P/T,4R/T) c) (P/4, RS/180) d) (P/8,S/R)

Ans given: d

6. If a/b=c/d, then the value of which of the following is equal to the value of (a^{2}+b^{2})/(c^{2}+d^{2})?

a) 1/2 b) a+b/c+d c)ab/cd d)a-b/c-d

Ans given: c

7. There are two numbers in the ratio P : Q. When 1 is subtracted from both numerator and denominator it becomes 2. which of the following can be the sum of P and Q?

a) 8 b)9 c)12 d)16

Ans Given: a

8. There are two persons A and B where A's present age is greater than B's present age. Which of the following will be the relation between the ratio of the squares of their ages after 7 years (X) and the ratio of their ages after 12 years(Y)?

a) X<Y b)X=Y c)X>Y d)X<=Y

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

n/a

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