ratio and proportion Model Questions & Answers, Practice Test for ssc cgl tier 1 2024

Answer: (a)

Let present age of mother and daughter be x and y.

2 years ago, x – 2 = 8(y – 2)

⇒x – 8y = – 14 ...(i)

1 year after, x + 1 = 5(y + 1)

⇒x – 5y = 4 ...(ii)

On solving equations. (i) and (ii), we get

y = 6 years and x = 34 years

Let after z years mother will be three times of her daughter.

34 + z = 3 (6 + z)⇒z = 8 years

Answer: (b)

Let a container contains x units of liquid and y units of liquid is taken out from it. If this operation is repeated n times, then the final quantity of the liquid in the container

is x $(1 - {y/x})^n$.

Therefore, from this equation, we have

24 = 54 $(1 - {y}/{54})^2$

(y = amount of acid initially drawn off)

or $(1 - {{y}/{54}})^2 = {{24}/{54}} = {4/9}$

or $(1 - {y}/{54}) = {2/3} or {{y}/{54}} = {1/3}$

or y = 18 litres

Answer: (a)

Let two numbers are 3x and 5x.

According to the question,

${3x - 9}/{5x - 9} = {12}/{23}$

⇒69x – 207 = 60x – 108

69x – 60x = 207 – 108

⇒9x = 99

∴ x = 11

∴ Second number = 5 × 11 = 55

Answer: (d)

Let the amount be Rs.x.

In first condition,

Q's part = ${5x}/{5 + 3} = 5/8$x

In second condition,

Q's part = ${3x}/{2 + 3} = 3/5$x

According to the question,

$5/8 x - 3/5 x$ = 10

∴ $x/{40}$ = 10⇒x = Rs.400

Answer: (b)

Let capacity of the vessel be x litres.

Therefore, ${x-4}/{4} = {1/2}$

∴ x = 6