Numerical Ability Test - 21

⇒ 3y = 4z

⇒ y/z = 4/3

⇒ y : z = 4 : 3

Now,

x : y = 3 : 2 and y = 4 : 3

making y equal in both ratios,

x : y = 6 : 4 and y = 4 : 3

So,

⇒ x : y : z = 6 : 4 : 3

So, the correct answer is option 4.

Given:

Charge on the first day = Rs. 15

Charge on the second day = Rs. 7.50

Charge on the third day = Rs. 2.50

Attendance ratio (first day : second day : third day) = 2 : 5 : 13

Formula Used:

Average charge per person = Total revenue / Total attendance

Calculation:

Let the attendance on the first day be 2x.

Attendance on the second day = 5x

Attendance on the third day = 13x

Total attendance = 2x + 5x + 13x

Total attendance = 20x

Revenue on the first day = 2x × 15

Revenue on the second day = 5x × 7.50

Revenue on the third day = 13x × 2.50

Total revenue = (2x × 15) + (5x × 7.50) + (13x × 2.50)

Total revenue = 30x + 37.5x + 32.5x

Total revenue = 100x

Average charge per person = Total revenue / Total attendance

Average charge per person = 5

The average charge per person for the whole show is Rs. 5.

Given:

The numbers are 15, 25, and 12.

Formula used:

If a, b, c, and d are in proportion, then a:b :: c:d or a/b = c/d.

Calculation:

15/25 = 12/x

⇒ 15 × x = 12 × 25

⇒ x = (12 × 25) / 15

⇒ x = 20

∴ The correct answer is option 4.

Given:

First number = 48

Second number = 24

Third proportional = x

Formula Used:

If a, b, and c are in continued proportion, then b² = a × c

Calculation:

Here, a = 48, b = 24, and c = x.

According to the formula:

24² = 48 × x

576 = 48 × x

x = 576 / 48

∴ The value of x is 12.

Given:

The monthly incomes of A, B, and C are in the ratio 2 : 9 : 3.

Their expenses are in the ratio 3 : 9 : 5.

A's saving is half of his total income.

Formula Used:

Savings = Income - Expenses

Calculation:

Let the monthly incomes of A, B, and C be 2x, 9x, and 3x respectively.

Let the monthly expenses of A, B, and C be 3y, 9y, and 5y respectively.

Given that A's saving is half of his income, so:

Saving of A = 2x / 2 = x

Savings = Income - Expenses

For A:

x = 2x - 3y

⇒ x = 2x - 3y

⇒ x = 3y

⇒ y = x / 3

For B:

Savings of B = Income of B - Expenses of B

Savings of B = 9x - 9y

⇒ Savings of B = 9x - 9(x / 3)

⇒ Savings of B = 9x - 3x

⇒ Savings of B = 6x

For C:

Savings of C = Income of C - Expenses of C

Savings of C = 3x - 5y

⇒ Savings of C = 3x - 5(x / 3)

⇒ Savings of C = 3x - (5x / 3)

⇒ Savings of C = (9x - 5x) / 3

⇒ Savings of C = 4x / 3

Now, the ratio of savings of A, B, and C:

Ratio = x : 6x : 4x / 3

⇒ Ratio = 3x : 18x : 4x

⇒ Ratio = 3 : 18 : 4

The savings of A, B, and C are in the ratio of 3 : 18 : 4.

Given:

Total Income = ₹6,00,000

Number of children = 4

Eldest son: share

Second son: share

Third son: share

Formula used:

Total shares = Sum of individual shares

Share of fourth son = Total Income - Sum of shares of first three sons

Calculations:

Step 1: Calculate share of eldest son.

Share of eldest son = = ₹1,00,000

Step 2: Calculate share of second son.

Share of second son = = ₹1,50,000

Step 3: Calculate share of third son.

Share of third son = = ₹3,00,000

Step 4: Calculate sum of shares.

Sum of shares = ₹1,00,000 + ₹1,50,000 + ₹3,00,000 = ₹5,50,000

Step 5: Calculate share of fourth son.

Share of fourth son = ₹6,00,000 - ₹5,50,000 = ₹50,000

Answer:

The fourth son will get ₹50,000.

Given:

a : b = c : d = e : f = 5 : 7

This implies:

a/b = c/d = e/f = 5/7

Thus, we can express a, c, e, b, d, f in terms of a common factor k:

a = 5k, b = 7k

c = 5m, d = 7m

e = 5n, f = 7n

Substitute these into the given ratio:

(3a + 5c + 11e) : (3b + 5d + 11f) = (3(5k) + 5(5m) + 11(5n)) : (3(7k) + 5(7m) + 11(7n))

Simplify the numerator and denominator:

Numerator = 15k + 25m + 55n

Denominator = 21k + 35m + 77n

Factor out 5 from the numerator and 7 from the denominator:

(15k + 25m + 55n) : (21k + 35m + 77n) = [5(3k + 5m + 11n)] : [7(3k + 5m + 11n)]

Cancel (3k + 5m + 11n) as it is common to both:

Ratio = 5 : 7

Final Answer: 5 : 7

Given:

Salaries ratio: Sunil : Basid : Vikram : Kuldeep = 3 : 7 : 8 : 13

Difference between salaries of Sunil and Basid = ₹2,000

Formula used:

If salaries are in the ratio a : b : c : d and difference between two salaries is given, we can use the ratio and the difference to find the actual salaries.

Calculations:

Let the common multiple be x.

Salary of Sunil = 3x

Salary of Basid = 7x

Difference between salaries of Sunil and Basid = 7x - 3x = 4x

4x = ₹2,000

⇒ x = 500

Salary of Vikram = 8x = 8 × 500 = ₹4,000

Salary of Kuldeep = 13x = 13 × 500 = ₹6,500

Difference between salaries of Vikram and Kuldeep = ₹6,500 - ₹4,000 = ₹2,500

∴ The correct answer is option 4.

Given:

a : b = 3 : 2

b : c = 3 : 2

Formula used:

To find a : b : c, we equalize the middle term (b) in both ratios.

Calculation:

a : b = 3 : 2

b : c = 3 : 2

To equalize b, find the LCM of 2 and 3, which is 6.

For a : b, multiply by 3: (3 × 3) : (2 × 3) = 9 : 6

For b : c, multiply by 2: (3 × 2) : (2 × 2) = 6 : 4

Now combine the ratios: a : b : c = 9 : 6 : 4

∴ a : b : c = 9 : 6 : 4

Given:

48 : x :: x : 75

x > 0

Formula Used:

In a proportion, the product of the means equals the product of the extremes.

Calculation:

48 : x :: x : 75

⇒ 48 × 75 = x × x

⇒ 48 × 75 = x²

⇒ 3600 = x²

⇒ x = 60

The value of x is 60.