Important Questions Test: Ratio & Proportion- 1 - CAT MCQ

Let the salaries of Ramesh, Ganesh and Rajesh in 2010 be 6x, 5x, 7x respectively
Let the salaries of Ramesh, Ganesh and Rajesh in 2015 be 3y, 4y, 3y respectively
It is given that Ramesh’s salary increased by 25% during 2010-2015,3y = 1.25*6x 
y = 2.5x
Percentage increase in Rajesh's salary = 7.5-7/7 = 0.07
= 7%

Let the number be x, 3x, 4x and 7x. Then, x + 3x + 4x + 7x = 75
⇒ 15x = 75 , x = 5
Required value = 7 * 5 = 35

Let 'p', 'q' and 'r' be the concentration of salt in Solutions A, B and C respectively.
It is given that three salt solutions A, B, C are mixed in the proportion 1 : 2 : 3, then the resulting Solution has strength 20%.
⇒ (p + 2q + 3r)/(1 + 2 + 3) = 20

⇒ p + 2q + 3r = 120     …….(1)
Also, if the proportion is 3 : 2 : 1, then the resulting Solution has a strength 30%.
⇒ (3p + 2q + r)/(3 + 2 + 1) = 30  

⇒ 3p + 2q + r = 180     ………..(2)
From equation (1) and (2), we get
⇒ q + 2r = 45
By observation, we find that q = r = 15 and p = 45.
So if we mix Solution B and C in any ratio we get the mixture with 15% concentration whereas A's strength = 45%.
Hence, the required ratio = 15/45 = 1 : 3

Correct Answer- Option A

Let B invested for n months

n = 3

Let their ages 5 years ago be 2x, 3x, 7x and 8x. Their ages now 2x + 5, 3x + 5, 7x + 5, 8x + 5.

Or, 20x + 20 = 140 ⇒ 2Ox = 120 ⇒ x = 6

Present age o f Nishu = 2 x 6 + 5 = 17 years

Present age o f mother = 7 x 6 + 5 = 47 years

Hence, required years (47 -17) years = 30 years

Given:

• The first wheel has 32 cogs.
• The second wheel has 54 cogs.
• The second wheel turns 80 times in 34 minutes (or 45 seconds).
• We want to find how many times the first wheel turns in 8 seconds.

Step 1: Determine the Gear Ratio

The gear ratio is determined by the number of cogs (teeth) on each wheel. Since the wheels work into each other, the gear ratio is:

Gear Ratio = 54/32 = 27/16

This means that for every 27 turns of the first wheel, the second wheel turns 16 times.

Step 2: Find the Rotational Speed of the First Wheel

Since the second wheel turns 80 times in 45 seconds, we can find its rotational speed in revolutions per second:

Rotational speed of second wheel = 80/45 = 16/9 turns per second

Using the gear ratio, we can find the rotational speed of the first wheel:

Rotational speed of first wheel = 27/16 × 16/9 = 3 turns per second

Step 3: Find the Number of Turns of the First Wheel in 8 Seconds

Since the first wheel turns 3 times per second, in 8 seconds it will turn:

3 × 8 = 24 turns

Answer

The first wheel turns 24 times in 8 seconds.

Correct Answer: (a) 24

Let Anil invested Rs X , then D heeraj’s investment = Rs 3x Let Dheeraj join him for n month

Total quantity of food at the beginning of the day
= (1600) (12) (1.2) 
Total number of soldiers left at the end of the day 1200
Now we have to calculate that for how long is available provision enough for the left-out soldiers
(1200) (x) (1.6)
(1600) (12) (1.2) = (1200) (x) (1.6)
Solving it for the value of x
We get x = 12
The provision is sufficient for 1200 soldiers for 12 days.