If (3/2)X = (5/7)Y = (6/5)Z, then what is X : Y : | Ratios and Proportions Questions & Answers

Q:

Pooja, Shipra and Mounika are three sisters .Pooja and Shipra are twins. The ratio of sum of the ages of Pooja and Shipra is same as that of Mounika alone. Three years earlier the ratio of age of Pooja and Mounika was 2:7 . what will be the age of Shipra 3 years hence?

A) 21 years	B) 16 years
C) 8 years	D) 12 years

Answer & Explanation Answer: C) 8 years

Explanation:

Since Pooja and Shipra are twins so their ages be same. Let their ages be x and age of Mounika be y , then

x+x = y -------(1)

and $\frac{x - 3}{y - 3} = \frac{2}{7} \Rightarrow 7 x - 2 y = 15$

Now, from equation (1),

7x - 4x = 15 => x = 5

So the age of Shipra 3 years hence will be 5+3 = 8 years

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Q:

Three cats are roaming in a zoo n such a way that when cat A takes 5 steps, B takes 6 steps and C takes 7 steps.But the 6 steps of A are equal to the 7 steps of B and 8 steps of C. what is the ratio of their speeds?

A) 140:144:147	B) 40:44:47
C) 15:21:28	D) 252:245:240

Answer & Explanation Answer: A) 140:144:147

Explanation:

Frequency of step of A:B:C = 5 : 6 : 7

But in terms of size of step, 6A = 7B = 8C

Therefore, Ratio of speeds of A, B and C = 5/6 : 6/7 : 7/8 = 140 : 144 : 147

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Q:

At a casino in mumbai, there are three tables A, B and C. The payoffs at A is 10:1, at B is 20:1 and at C is 30:1. If a man bets Rs 200 at each table and win at two of the tables, what is the maximum and minimum difference between his earnings can be?

A) Rs.2500	B) Rs.2000
C) Rs.4000	D) None of these

Answer & Explanation Answer: C) Rs.4000

Explanation:

Maximum earning will be only when he will won on the maximum yielding table.

A ----> 10:1

B ----> 20:1

C ----> 30:1

i.e, he won on B and C but lost on A

20 x 200 + 30 x 200 -1 x 200 = 9800

minimum earning will be when he won on table A and B and lose on that table 3.

Therefore, 10 x 200 + 20 x 200 - 1 x 200 = 6000-200 = 5800

Therefore, Difference= 9800 - 5800 = 4000

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12 7526

Q:

The ratio of students in a coaching preparing for B.tech and MBA is 4 : 5. The ratio of fees collected from each of B.tech and MBA students is 25 : 16. If the total amount collected from all the students is 1.62 lakh, what is the total amount collected from omly MBA aspirants?

A) Rs. 62,000	B) Rs. 72,000
C) Rs. 82,000	D) None of these

Answer & Explanation Answer: B) Rs. 72,000

Explanation:

The ratio of fees collected from B.Tech : MBA = 4x * 25y : 5x * 16y

= 100xy : 80xy

= 5xy : 4 xy = 5k : 4k

The amount collected only from MBA students = $\frac{4}{9} \times 1.62 l a k h$ = Rs. 72,000

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18 13403

Q:

A, B and C have amounts in the ratio of 3 : 4 : 5. First B gives 1/4th to A and 1/4th to C then C gives 1/6th to A. Find the final ratio of amount of A, B and C respectively.

A) 4:3:5	B) 5:4:3
C) 3:4:5	D) 5:2:5

Answer & Explanation Answer: D) 5:2:5

Explanation:

A B C

3x 4x 5x

(3x+x) 2x (5x+x) (B Gives 1/4 to A and 1/4 to C)

=4x 2x 6x

(4x+x) 2x 5x ( C Gives 1/6 to A)

=5x 2x 5x

Therefore, 5 : 2 : 5

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Q:

6 pumps of kirlosker can fill a tank in 7 days and 2 similar pumps of USHA can fill the same tank in 18 days. what is the ratio of the efficiency of a kirlosker pump and a USHA pump?

A) 6:7	B) 7:6
C) 7:54	D) None of these

Answer & Explanation Answer: A) 6:7

Explanation:

The number of days required by a single kirlosker pump to fill the tank = 6 x 7 =42 days and the number of days required by a single USHA pump to fill the same tank = 2 x 18 =36 days.

Now , since efficiency is inversely proportional to the number of days. Hence,

$\frac{E f f i c i e n c y o f o n e K - p u m p}{E f f i c i e n c y o f U - p u m p} = \frac{36}{42} = \frac{6}{7}$

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Q:

For any two numbers m , n ; (m+n) : (m-n) : mn = 7: 1: 60 . Find the value of 1/m : 1/n

A) 4:3	B) 8:7
C) 3:4	D) 7:8

Answer & Explanation Answer: C) 3:4

Explanation:

$\frac{m + n}{m - n} = \frac{7 x}{x} \Rightarrow \frac{m}{n} = \frac{4 x}{3 x}$

Again $m n = 12 x^{2}$

and mn =60x

so, $60 x = 12 x^{2} \Rightarrow x = 5$

=> m= 20 and n= 15

Hence, $\frac{1}{m} : \frac{1}{n} = \frac{1}{20} : \frac{1}{15} = 3 : 4$

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Q:

The concentration of petrol in three different mixtures (petrol and kerosene) is 1/2 , 3/5 and 4/5 respectively. If 2 litres, 3 litres and 1 litre are taken from these three different vessels and mixed. what is the ratio of petrol and kerosene in the new mixture?

A) 4:5	B) 3:2
C) 3:5	D) 2:3

Answer & Explanation Answer: B) 3:2

Explanation:

Concentration of petrol in A B C

1/2 3/5 4/5

Quantity of petrol taken from A = 1 litre out of 2 litre

Quantity of petrol taken from B = 1.8litre out of 3 litre

Quantity of petrol taken from C = 0.8 litre out of 1 litre

Therefore, total petrol taken out from A, B and C = 1+1.8+0.8 =3.6 litres

So, the quantity of kerosen =(2+3+1) - 3.6 =2.4 litre

Thus, the ratio of petrol to kerosene = 3.6/2.4 = 3/2

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A) 105 : 50 : 84	B) 24 : 25 : 32
C) 15 : 21 : 25	D) 20 : 42 : 25

If (3/2)X = (5/7)Y = (6/5)Z, then what is X : Y : Z?

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