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

Q:

Pencils, Pens and Exercise books in a shop are in the ratio of 10: 2 : 3. If there are 120 pencils, the number of exercise books in the shop is:

A) 26	B) 36
C) 46	D) 56

Answer & Explanation Answer: B) 36

Explanation:

Let Pencils = 10x, Pens = 2x & Exercise books = 3x. Now, 10x = 120 hence x = 12.
Number of exercise books = 3x = 36.

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44 18434

Q:

The third proportional to $(x^{2} - y^{2})$ and $(x - y)$ is :

A) (x + y )	B) (x - y)
C) (x + y) / ( x - y)	D) (x -y) / ( x + y)

Answer & Explanation Answer: D) (x -y) / ( x + y)

Explanation:

Let the third proportional to $(x^{2} - y^{2})$ and $(x - y)$ be z. Then,

$(x^{2} - y^{2}) : (x - y) : : (x - y) : z$

$= > (x^{2} - y^{2}) * z = {(x - y)}^{2}$

=> z= $\frac{{(x - y)}^{2}}{(x^{2} - y^{2})} = \frac{(x - y)}{(x + y)}$

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65 15762

Q:

The sum of three numbers is 98. If the ratio of the first to second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is:

A) 10	B) 20
C) 30	D) 40

Answer & Explanation Answer: C) 30

Explanation:

Let the three parts be A, B, C. Then,

A : B = 2 : 3 and B : C = 5 : 8 = $(5 * \frac{3}{5}) : (8 * \frac{3}{5})$ = $3 : \frac{24}{5}$

$\Rightarrow$ A : B : C = 2 : 3 : => = 10 : 15 : 24

$\Rightarrow$ B = $\frac{24}{5}$ = 30

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45 14565

Q:

Salaries of Ravi and Sumit are in the ratio 2:3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40:57. What is Sumit's salary?

A) 38000	B) 46800
C) 36700	D) 50000

Answer & Explanation Answer: A) 38000

Explanation:

Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.
Then,
(2x+4000) / (3x+4000) = 40 / 57
⇒ 57 × (2x + 4000) = 40 × (3x+4000)
⇒ 6x = 68,000
⇒ 3x = 34,000
Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000

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429 110011

Q:

Seats for Mathematics, Physics and Biology in a school are in the ratio 5:7:8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats ?

A) 1:2:3	B) 2:3:4
C) 3:4:5	D) 4:5:6

Answer & Explanation Answer: B) 2:3:4

Explanation:

Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).
⇒ [(140/100) × 5x],[(150/100) × 7x] and [(175/100) × 8x]
⇒ 7x, 21x/2 and 14x.

⇒ The required ratio =7x : 21x/2 : 14x
⇒ 14x : 21x : 28x
⇒ 2 : 3 : 4

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162 50531

Q:

A sum of Rs.312 was divided among 100 boys and girls in such a way that the boy gets Rs.3.60 and each girl Rs. 2.40 the number of girls is

A) 35	B) 40
C) 45	D) 50

Answer & Explanation Answer: B) 40

Explanation:

Step (i): Let x be the number of boys and y be the number of girls.
Given total number of boys and girls = 100
x+y=100 -------------- (i)

Step (ii): A boy gets Rs. 3.60 and a girl gets Rs. 2.40
The amount given to 100 boys and girls = Rs. 312
3.60x + 2.40y = 312 -------------- (ii)

Step (iii):
Solving (i) and (ii)
3.60x + 3.60y = 360 --------- Multiply (i) by 3.60
3.60x + 2.40y = 312 --------- (ii)
1.20y = 48
y = 48 / 1.20
= 40

$\Rightarrow$ Number of girls = 40

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341 80953

Q:

Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

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

Answer & Explanation Answer: C) 4:5

Explanation:

Let the third number be x.

Then, first number = 120% of x =120x/100 = 6x/5

Second number =150% of x = 150x/100 = 3x/2

Ratio of first two numbers = 6x/5 : 3x/2 = 12x : 15x = 4 : 5

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600 182958

Q:

A mixture contains alcohol and water in the ratio 4 : 3. If 5 liters of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture.

A) 10	B) 12
C) 15	D) 18

Answer & Explanation Answer: A) 10

Explanation:

Let the quantity of alcohol and water be 4x litres and 3x litres respectively

4x/(3x+5) = 4/5

20x = 4(3x+5)

8x = 20

x = 2.5

Quantity of alcohol = (4 x 2.5) litres = 10 litres.

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336 62593

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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