Important Questions Test: Ratio & Proportion- 2 - CAT MCQ

Area of semicircle = (1/2)πr²
Area of sector = (θ/360)πr²

V ∝ W², V = KW²
Where, V = Value of diamond, W = weight of diamond and K = constant
⇒ 10000 = K.(10)²
⇒ K = 100
Hence, V = 100 x 4² = 1600
also, V = 100 x 6² = 3600
Net loss = Rs.(10000 - 5200) = Rs 4800 i.e., 48%

► Let the fare of 1st, 2nd and 3rd class be 10x, 8x, and 3x respectively.
► Let the no. of passengers of 1st, 2nd and 3rd class be 3y, 4y and 10y respectively. 
Then 30xy + 32xy + 30xy = 16100
⇒ 92xy = 16100
Hence xy = 175
Required amount = 32xy = 32 x 175 = 5600 

► Price of one goat = Rs 70 ⇒ Price of 9 goats = 9 x 70 = Rs 630
► Price of 14 sheeps = Rs 630 
⇒ Price of 1 sheep = Rs 630/14 = Rs 45 ⇒ Price of 50 sheep = Rs 45 x 50 = Rs 2250
► Price of 10 oxen = 2250 ⇒ Price of 1 oxen = 225 ⇒ Price of 8 oxen  = 1800
► Price of 6 dogs = 1800 ⇒ Price of 1 dog = 300 ⇒ Price of 5 dog = 1500
► Price of two horses = 1500 ⇒ Price of one horse = 750

► Let the 1^stno. = A = x
2^nd no.= B , 3^rd no.= C , 4^th no. = D
► A:B = 2:3
    A/B = 2/3
    x/B = 2/3
    B = 3x/2
► B:C = 5:6
    (3x/2)/C = 5/6
    C = (6*3x)/2*5 = 9x/5
    C = 9x/5
► C:D = 8:9
    9x/5/D = 8/9
    D = (9x*9)/8*5 = 81x/40
    D = 81x/40
► A + B + C + D = 253. (Given)
    ⇒ x + 3x/2 + 9x/5 + 81x/40 = 253
    ⇒ (40x+ 60x+ 72x+81x)/40 = 253
    ⇒ 253x = 253*40
    ⇒ X = (253*40)/253 = 40
    ⇒ 1st no.(A) = X = 40
    ⇒ 2nd no.(B) = 3x/2 =( 3 × 40)/2 = 60
    ⇒ 3rd no.(C) = 9x/5 = (9×40)/5 = 72
    ⇒ 4th no.(D) = 81x/40 =( 81×40/)/40 = 81
► Average of numbers = sum of observations/ total no.of observations
► Average of 2nd no. & 3rd no.= (60+72)/2 = 132/2 = 66

► Given that a man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal.
► We are to find the total number of notes he has.
► Let x represents the number of notes of each of the three denominations.
► Then, according to the given information, we have
⇒ 1.x + 5.x + 10.x = 480
⇒ x + 5x + 10x = 480
⇒ 16x = 480
⇒ x = 30
► Therefore, the total number of notes is given by 
⇒ x + x + x = 3x = 3*30 = 90

► Let A, B, C invested Rs 4x, Rs x, Rs 15x respectively.
► According to question, Ratio of their investments for 1 year
= (4x*3 + 2x*3 + x*3 + x/2*3) : (x*3 + 2x*3 + 4x*3 + 8x*3) : (15x*12)
⇒ 45x/2 : 45x : 180x
⇒ 45 : 90 : 360
⇒ 1 : 2 : 8
Total profit = (11/2)*22000 = Rs 121000

CP = 75

► According to question, A:B:C:D = 6:5:10:14
► Now in D there are 70 chapters
Therefore, A:B:C:D = 30:25:50:70      [ Multiplying Each by 5 ]
L.C.M of 30, 25, 50, 70 is 1050
So each part should have 1050 pages.
So total pages = 4 x 1050 = 4200 ans.

► Let their present ages be 2x and 3x.
Given that

10x + 5N = 9x + 3N
X = -2N which 18 not possible.
Hence, correct option is (d).

► Number of apples/Number of guavas = Number of guavas/Number of oranges
► (Number of guavas)² = Number of apples x Number of oranges.
► This gives us a hint that Number of apples x Number of oranges should be a prefect square.
Now start using the options.
Option (b) satisfies the relationship (16/20 = 20/25)

Given:

Total coin = 220

Total money = Rs. 160

There are thrice as many 1 Rupee coins as there are 25 paise coins.

Concept used:

Ratio method is used.

Calculation:

Let the 25 paise coins be 'x'

So, one rupees coins = 3x

50 paise coins = 220 – x – (3x) = 220 – (4x)

According to the questions,

3x + [(220 – 4x)/2] + x/4 =160

⇒ (12x + 440 – 8x + x)/4 = 160

⇒  5x + 440 = 640

⇒ 5x = 200

⇒ x = 40

So, 50 paise coins = 220 – (4x) = 220 – (4 × 40) = 60

∴ The number of 50 paise coin is 60.

Total cost = Fixed cost + Variable cost

Variable cost = k × b
where, b = number of boarders and k = variable cost per boarder.

Total cost = FC + kb

Total collection = 1600b

Case 1: Total profit = 200 × 50 = 1600 × 50 – (FC + k × 50)   …(1)
Case 2: Total profit = 250 × 75 = 1600 × 75 – (FC + k × 75)   …(2)

(2) - (1), we get
18750 – 10000 = 1600 × 25 - 25k
⇒ k = 1250 and FC = 7,500 

Now, total profit when there are 80 boarders = 1600 × 80 – (7500 + 1250 × 80) = 20,500

Alternately,
Total cost when there are 50 students = (1600 – 200) × 50 = 70,000
Total cost when there are 75 students = (1600 – 250) × 75 = 1,01,250

Due to 25 students cost increases by (101250 - 70000) = 31250
∴ Due to 5 students cost increases by = 31250/5 = 6250

∴ Total cost when there are 80 students = 1,01,250 + 6250 = 1,07,500
Total revenue for 80 students = 1600 × 80 = 1,28,000

∴ Profit = 1,28,000 – 1,07,500 = 20,500.

Hence, option (d).

It is given that the scores of Anjali, Mohan and Rama after review were in the ratio 11 : 10 : 3

So, let their values be 11x, 10x and 3x respectively.

It is known that their score increased by 6 after review.

So, scores before review = 11x - 6, 10x - 6 and 3x - 6 respectively

Now, from the data given : (11x - 6 + 10x - 6) × 1/12 = 3x - 6

⇒ 21x - 12 = 36x - 72

⇒ 60 = 15x

⇒ x = 4

So, marks after revision are 44, 40 and 12 respectively.

Therefore, Anjali's score exceeded Rama's by 44 - 12 = 32 marks

Hence, option (b).

C₅ – C₁ = 19.
∴ 100x - 81x = 19
⇒ x = 1

∴ Total profit = 81x + 90x + 72x + 95x + 100x = 438x = 438 crore.

Hence, option (a).