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Q:

Ten years ago A was half of B in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages

A) 15	B) 25
C) 35	D) 45

Answer & Explanation Answer: C) 35

Explanation:

Let A's age 10 years ago = x years.
Then, B's age 10 years ago = 2x years.
(x + 10) / (2x+ l0) = 3/4
=> x = 5.
So, the total of their present ages =(x + 10 + 2x + 10)
= (3x + 20) = 35 years.

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Filed Under: Problems on Ages

Q:

Sachin is younger than Rahul by 7 years. If the ratio of their ages is 7:9, find the age of Sachin

A) 24.5	B) 25.5
C) 26.5	D) 27.5

Answer & Explanation Answer: A) 24.5

Explanation:

If Rahul age is x, then Sachin age is x - 7,

so, (x-7)/x =7/9

$\Rightarrow$ 9x - 63 = 7x
$\Rightarrow$ 2x = 63
$\Rightarrow$ x = 31.5

So Sachin age is 31.5 - 7 = 24.5

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Filed Under: Problems on Ages

Q:

A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is :

A) 9:5	B) 2:3
C) 4:7	D) 5:6

Answer & Explanation Answer: A) 9:5

Explanation:

Dog : Hare = (3*3) leaps of hare : 5 leaps of hare = 9 : 5.

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Filed Under: Ratios and Proportions

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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Filed Under: Ratios and Proportions

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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Filed Under: Ratios and Proportions

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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Filed Under: Ratios and Proportions

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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Filed Under: Ratios and Proportions

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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Filed Under: Ratios and Proportions

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