# Ratio, Proportion and Variation 1

**Q1. If a/b = b/c = c/d, then the value of sqrt [(a^5 + b^2c^2 + a^3c^2)/(b^4c + d^4 + b^2cd^2)]a. a/d b. b/d c. c/d d. all of these e. None of the these**

Q2. We have 100L of solution of milk and water in which the ratio of milk and water is 3 : 2. we add 25L of milk to this solution and then throw 25 L of the solution out. If the same process is done two more times, what would be the percentage of milk in the solution?

a. 83.675 b. 74.4 c. 79.52 d. 86.57

Q3. There are 5 glasses of the same capacity. The glasses are filled with water, such that the ratio of the quantities of water in the 5 glasses is 3 : 4 : 5 : 6 : 7. The total quantity of water in the 5 glasses is 3/5 of the total capacity of the 5 glases. How many glasses have at least half of their capacity filled with water?

a. 3 b. 4 c. 2 d. 5

Q4. P, Q and R are distinct positive real numbers.

[ P^4 (Q^2 + R^2) + Q^4 (P^2 + R^2) + R^4 (Q^2 + P^2) ] / (PQR)^2 must be more than

a. 6 b. 7 c. 8 d. None of these

Q5. If y/(x-z) = (y+x)/z = x/y ; Find the ratio x : y : z

a. 4 : 2 : 3

b. 2 : 3 : 4

c. 4 : 3 : 2

d. 3 : 4 : 2

Q6. Three positive numbers a b and c are such that abc/(a+b+c) = ab + bc + ca.

What is the value of (a+b+c)/a + (b+c+a)/b + (c+a+b)/c ?

a. 0

b. a+b+c

c. a+b+c+abc

d. None of these

Q7. A kangaroo purses a hare and their leaps are in the ratio 10 : 1. The kangaroo takes 1 leap in the time the hare takes 5. If the hare is 50 leaps (of itself) ahead of the kangaroo. How many leaps does the kangaroo have to make to catch up?

a. 5 leaps b. 10 leaps c. 50 leaps d. 25 leaps

Q8. The Onion imported from china and US are known as “Chinapiyaj” and “Amipiyaj” respectively.

Last year the prices of Chinapiyaj and Amipiyaj were in the ratio 3 : 4. The prices of Chinapiyaj last year and this year is in the ratio 4 : 5 and that of Ampiyaj is in the ratio 8 : 9. This year, a kg of Chinapiyaj and a kg of Amipiyaj together cost Rs. 66.

How much does a kg of Chinapiyaj Cost this year?

a. Rs. 24 b Rs. 36 c. Rs. 30 d. Rs. 32

Q9. The time taken by a jet, to reach a certain place while flying at a speed, slower by 300 m/h than the normal, is double the time taken by it while flying at a speed faster by 300 m/h than normal. What is the ratio of the ‘delay time’ while flying slower to the ‘early time’ while flying faster?

a. 3 : 2 b. 1 : 2 c. 2 : 1 d. cannot be determined

Q10. Given that a + b varies as c + 1/c and that a –b varies as c – 1/c, find the relation between a, b and c provided c = 2 when a =3 and b =1.

a. a = 22c/15 + 2/15c

b. b = 22c/15 + 2/15c

c. c = 22a/15 + 2/15a

d. None of the above

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The easiest way to solve such questions is by taking some values of a, b,c and d.

for ex. for this case take

a = 1

b = 2

c = 4

d = 8

and find out the value of the expression. i am getting the answer as e

Q4. P, Q and R are distinct positive real numbers.

[ P^4 (Q^2 + R^2) + Q^4 (P^2 + R^2) + R^4 (Q^2 + P^2) ] / (PQR)^2 must be more than

a. 6 b. 7 c. 8 d. None of these

ans is (d) because sume must be more than 5

Q6. Three positive numbers a b and c are such that abc/(a+b+c) = ab + bc + ca.

What is the value of (a+b+c)/a + (b+c+a)/b + (c+a+b)/c ?

a. 0

b. a+b+c

c. a+b+c+abc

d. None of these

ans(d) ans=1

Little Star

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**@jigarI get nother soln...Plz check it.... Q1. If a/b = b/c = c/d, then the value of sqrt [(a^5 + b^2c^2 + a^3c^2)/(b^4c + d^4 + b^2cd^2)]a. a/d b. b/d c. c/d d. all of these e. None of the these**

Soln. Let a/b=b/c=c/d=k.

=>a=dk^3,b=dk^2,c=dk...

By puttin d values: [(a^5 + b^2c^2 + a^3c^2)/(b^4c + d^4 + b^2cd^2)]

=k^6(test it)

sqrt [(a^5 + b^2c^2 + a^3c^2)/(b^4c + d^4 + b^2cd^2)]=k^3=a/d

So option (a) is correct....

Giv ur best to d world.

Nd d best will cm back to u....

Regards,

Dipanjan......

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Q1 is easily solved by replacing using k as constant..

Q2 is solved by basic math..but i do not know of a easy way to do this..can any one suggest how to...there has to be some exponential series involved as the process can be repeated any number of times...plz do provide an easy way :)

Thanks in adv

Nikhil

What is the answer for Question 1 ?

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give the answer with complete solution

ans

2-C

3-A

5-A

7-B

8-C

9-D

10-A

can any one correct me its right or wrong?, for remaining problem me r working on it

Little Star

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