Compound Ratios MCQ Quiz - Objective Question with Answer for Compound Ratios - Download Free PDF

Calculation

Total toffies B and C has = 60 – 25 = 35

Let total toffies B has = x

So, total toffies C has = x – 5

ATQ, [2x – 5] = 35

Or, 2x = 40, x = 20

Let y toffies added with C to found resultant ratio

So, [15 + y]/ 20 = [6/4]

Or, 15 + y = 30

So, y = 15

Given:

\(\frac{15}{18}=\frac{x}{6}=\frac{10}{y}=\frac{z}{30}\)

Formula Used:

If \(\frac{a}{b} = \frac{c}{d}\), then ad = bc

Calculation:

\(\frac{15}{18} = \frac{x}{6}\)

⇒ \(15 \times 6 = 18 \times x\)

⇒ x = 5

\(\frac{15}{18} = \frac{10}{y}\)

⇒ \(15 \times y = 18 \times 10\)

⇒ y = 12

\(\frac{15}{18} = \frac{z}{30} \)

⇒ \(15 \times 30 = 18 \times z\)

⇒ z = 25

Value of x + y + z = 5 + 12 + 25 = 42

∴ The value of x + y + z is 42

Given:

The total amount is divided between A, B, and C in the ratio 8 : 4 : 3.

A divides his share between D and E in the ratio 9 : 7.

Formula used:

Profit = Time × Investment

Calculation:

Let the total amount of money be S.

A's share = (8 / (8 + 4 + 3)) × S = (8 / 15) × S

B's share = (4 / (8 + 4 + 3)) × S = (4 / 15) × S

C's share = (3 / (8 + 4 + 3)) × S = (3 / 15) × S

Now, A divides his share between D and E in the ratio 9 : 7.

So, D's share from A = (9 / (9 + 7)) × A's share = (9 / 16) × (8 / 15) × S

⇒ D's share = (72 / 240) × S = (3 / 10) × S

Now, we need to find the ratio of C's share to D's share:

C's share : D's share = (3 / 15) × S : (3 / 10) × S

⇒ Ratio = (3 / 15) × (10 / 3) = 2 / 3

∴ The ratio of C's share to D's share is 2 : 3.

Given:

Total amount = Rs. 2730

A = (B + C)/2

B = 2/5 (A + C)

Formula used:

Ratio and Proportion

Calculations:

From the given information,

2A = B + C and 5B = 2A + 2C

Substituting 2A in the second equation,

5B = B + C + 2C

⇒ B = 3C/4

Now, substitute B back into 2A = B + C

2A = 3C/4 + C

⇒ A = 7C/8

Now, A + B + C = 2730

Substituting A and B in terms of C,

7C/8 + 3C/4 + C = 2730

⇒ 7C + 6C + 8C = 2730 * 8

⇒ 21C = 21840

⇒ C = 21840/21 = 1040

Similarly,

⇒ A = 7C/8 = 7 × 1040/8

A = 910

Difference = C - A = 1040 - 910 = 130

∴ C's share is Rs. 130 more than A's.

Given:

Total amount = Rs. 2730

A = (B + C)/2

B = 2/5 (A + C)

Formula used:

Ratio and Proportion

Calculations:

From the given information,

2A = B + C and 5B = 2A + 2C

Substituting 2A in the second equation,

5B = B + C + 2C

⇒ B = 3C/4

Now, substitute B back into 2A = B + C

2A = 3C/4 + C

⇒ A = 7C/8

Now, A + B + C = 2730

Substituting A and B in terms of C,

7C/8 + 3C/4 + C = 2730

⇒ 7C + 6C + 8C = 2730 * 8

⇒ 21C = 21840

⇒ C = 21840/21 = 1040

Similarly,

⇒ A = 7C/8 = 7 × 1040/8

A = 910

Difference = C - A = 1040 - 910 = 130

∴ C's share is Rs. 130 more than A's.

Given 

Total rupees = Rs 750 

Calculation

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 

Given:

(a + 3b) : (2a + 4b) = 3 : 5

Formula used:

if \(\frac{a}{b} = \;\frac{c}{d}\)

then, \(\;\;\frac{{a - b}}{{a + b}} = \;\frac{{c - d}}{{c + d}}\)

Calculation:

\(\frac{{\left( {a + 3b} \right)}}{{\left( {2a + 4b} \right)}} = \;\frac{3}{5}\)

⇒ 5 × (a + 3b) =  3 × (2a + 4b) 

⇒ 5a + 15b = 6a + 12b

⇒ a = 3b

⇒ \(\frac{a}{b} = \;\frac{3}{1}\)

⇒ \(\frac{{a - b}}{{a + b}} = \;\frac{{3 - 1}}{{3 + 1}}\)

⇒ \(\frac{{a - b}}{{a + b}} = \;\frac{2}{4} = \;\frac{1}{2}\)

⇒ (a - b) : (a + b) = 1 : 2

Given:

The products of the numbers of Rs. 10 and Rs. 5 coins, the numbers of Rs. 5 and Rs. 2 coins, and the numbers of Rs. 2 and Rs. 10 coins is 3 ∶ 4 ∶ 2

Calculation:

Ratio = 3 : 4 : 2

By multiplying with 6 we get,

18 : 24 : 12

We write 18 : 24 : 12 as (6 × 3) : (6 × 4) : (4 × 3)

So, from this we can assume the number of 10 rupee coins are 3, number of 5 rupee coins are 6 and number of 2 rupee coins are 4

So, minimum possible amount could be 10 × 3 + 5 × 6 + 2 × 4

⇒ 30 + 30 + 8

⇒ 68

∴ The required answer is 68.

Given : 

a + b + c = 1904

a ∶ (b + c) = 3 ∶ 13

b ∶ (a + c) = 5 ∶ 9

Calculation : 

⇒ a ∶ (b + c) = 3 ∶ 13   --------------(1)

⇒ b  ∶ (a + c) = 5 ∶ 9     ------------------(2)

By adding one on both LHS and RHS of both the equations,

⇒ a + b + c : b + c = 16 : 13

⇒ a + b + c : a + c = 14 : 9 

Now making (a : b : c) same we get

⇒ a + b + c : b + c = 16 : 13 = 16 × 7 : 13 × 7 = 112 :  91

⇒ a + b + c : a + c = 14 : 9 = 14 × 8 : 9 × 8 = 112 : 72

So, 112x = 1904

⇒ x = 1904/112 = 17

Now, b + c = 91 × 17 = 1547

⇒ a + c = 72 × 17 = 1224

Now a + b + c = 1904

⇒ a + 1547 = 1904, a = 357

⇒ b + 1224 = 1904, b = 680

Now 357 + 680 + c = 1904

⇒ c = 1904 - 357 - 680 = 867

∴ The correct answer is 867.

Alternate Method a + b + c = 1904

a ∶ (b + c) = 3 ∶ 13

a/(b + c)  + 1 = (3/13) +1

a+ b + c /(b + c) = 16/13  

1904/(b + c) = 16/13 

b+ c = 1547  (i)

similarly,
b ∶ (a + c) = 5 ∶ 9
a+ b + c /(a + c) = 14/9     

1904/(a + c) = 14/9 

a+ c = 1224  (ii)

adding Equation (i) & (ii)

a + b + c + c = 1547 +1224

1904 + c = 2771

c = 867

∴ The correct answer is 867.

⇒ (1/2) ∶ (2/3) ∶ 3 ∶ 4 = 3 ∶ 4 ∶ 18 ∶ 24

a : (b + c) = 1 : 3      ---(1)

c : (a + b) = 5 : 7      ---(2)

Multiply by 3 in equation (1)

a : (b + c) = 3 : 9      ---(3)

From equation (2) and equation (3)

c = 5 and a = 3 

a + b = 7

3 + b = 7

b = 7 – 3 = 4

Now,

b : (c + a)

⇒ 4 : (5 + 3)

⇒ 4 : 8

Given

sum divided between A, B and C is 3780

Calculation

let the share of A, B and C is 5x , 2x and 4x after decrease

so, original share of A, B and C is (5x + 130), (2x + 150) and (4x + 200)

5x + 130 + 2x + 150 + 4x + 200 = 3780

⇒ 11x + 480 = 3780

⇒ 11x = 3780 - 480

⇒ 11x = 3300

⇒ x = 300

Original share of C = (4x + 200)

⇒ (4 × 300 + 200)

⇒ 1200 + 200

⇒ 1400

∴ The original share of C is 1400.

Let the new price of the pastry be Rs. ‘x’

⇒ The ratio of old to the new price of pastry = 48 ∶ x

Now,

⇒ The ratio of earning of bakery = Ratio of sale of pastries × Ratio of the price of pastries

⇒ 4 ∶ 5 = 5 ∶ 8 × 48 ∶ x

∵ The compound ratio of ratios a ∶ b and c ∶ d is ac ∶ bd

⇒ 4/5 = 30/x

⇒ x = 30 × 5/4 = Rs. 37.50

GIVEN:

Sum of three numbers is 160 and these numbers are in the ratio of 1 : 3 : 4.

CONCEPT:

Basic ratio concept.

CALCULATION:

Suppose the numbers are x, 3x and 4x respectively.

So,

x + 3x + 4x = 160

8x = 160

x = 20

Now,

Given:

(8/5) P = (7/4) Q = (4/3) R

Calculation

Let, (8/5) P = (7/4) Q = (4/3) R = k

P = 5/8 k, Q = 4/7 k, R = 3/4 k

Then, P ∶ Q ∶ R = 5/8 k ∶  4/7 k ∶ 3/4 k

Now, let us take the LCM of (8, 7, 4) = 56

⇒ P ∶ Q ∶ R = (5 × 7) ∶ (4 × 8) ∶ (3 × 14)

Then P : Q : R = 35 : 32 : 42

∴  The required ratio of P: Q: R = 35 : 32 : 42.