Test: Ratio & Proportion - 1 - UCAT MCQ

Let's denote A's income as x.

According to the given information:

B's income = 2x

C's income = 3x

The total income of A, B, and C is Rs. 60,000:

x + 2x + 3x = 60,000

6x = 60,000

x = 10,000

Therefore,

A's income is Rs. 10,000.

∴ B 's income is 2x = 2 × 10,000 = Rs. 20,000.

Simple Interest for 1 year = Rs. (854 − 815)

= Rs. 39

Simple Interest for 3 years = Rs. 39 × 3

⇒ Rs. 117

Principal = Rs. 815 − Rs. 117

⇒ Rs. 698

∴ The sum is Rs. 698.

Let the salary of P = 5x

Q = 3x and R = 7x

According to the question, 

R gets Rs. 3600 more than Q,

⇒ 7x = 3x + 3600

⇒ 4x = 3600 ⇒ x = 900

∴ The salary of P = 5 × 900 = Rs 4500

u : v = 4 : 7 and v : w = 9 : 7

To make ratio v equal in both cases 

We have to multiply the 1st ratio by 9 and 2nd ratio by 7

u : v = 9 × 4 : 9 × 7 = 36 : 63    ----(i)

v : w = 9 × 7 : 7 × 7 = 63 : 49    ----(ii)

Form (i) and (ii), we can see that the ratio v is equal in both cases 

So, Equating the ratios we get,

u ∶ v ∶ w = 36 ∶ 63 ∶ 49

⇒ u ∶ w = 36 ∶ 49

When u = 72,

⇒ w = 49 × 72/36 = 98

∴ Value of w is 98

Let the number of coins of ₹ 2, ₹ 5 and ₹ 10 be 6x, 9x, and 10x respectively

⇒ (2 × 6x) + (5 × 9x) + (10 × 10x) = 785

⇒ 157x = 785

∴ x = 5

Number of coins of ₹ 5 = 9x = 9 × 5 = 45

∴ 45 coins of ₹ 5 are in the bag

60 Rupees = 60 × 100 = 6000 paise

⇒ 5 × 3x + 10 × 2x + 25 × 1x = 6000

⇒ 15x + 20x + 25x = 6000

⇒ 60x = 6000

⇒ x = 100

∴ Number of 5 paise coins = 3x = 3 × 100 = 300

A : B = 5 : 2 

B : C = 7 : 13 

A : B : C = 5 × 7 : 2 × 7 : 2 × 13 = 35 : 14 : 26 

Total Sum = 750 

⇒ 35 x + 14x + 26x = 750 

⇒ x = 10 

So, A's share = 35 × 10 = Rs 350 

∴ The required answer is Rs 350 

Let age of c be x

⇒ Age of B = 2x

⇒ Age of A = 2x + 2

⇒ x + 2x + 2x + 2 = 27

⇒ 5x = 25

⇒ x = 5

∴ The age of B is 5 × 2 = 10 years.

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.

a : b = 3 : 2 now check which options satisfied this ratio

1) a : b = 100 : 75 = 4 : 3 not equal to 3 : 2

2) a : b = 100 : 30 = 10 : 3 not equal to 3 : 2

3) a : b = 105 : 70 = 21 : 14 = 3 : 2 which is equal to 3 : 2

4) a : b = 105 : 35 = 21 : 7 = 3 : 1 which is not equal to 3 : 2

hence option 3 is correct option