Explanation

3x:2X

3X=2X+5 3

X-2X=5

X=5

Age of younger one is 2X

 X is 5 that is equal to 5×2=10

ND11-3-2023

SH25-8-2023

Explanation

The mean proportional between two numbers a and b is a number x such that: a : x :: x : b

In this case, we want to find the mean proportional between 64 and 81.

Let's set up the proportion: 64 : x :: x : 81

We can rewrite this as: 64/x = x/81

Cross-multiplying, we get: 64 × 81 = x^2

Simplifying, we get: 5184 = x^2

Taking the square root of both sides, we get:

x = √5184

x = 72

So, the mean proportional between 64 and 81 is 72.

Explanation

Let's break down the problem step by step:

Step 1: Express the initial number of boys and girls using the given ratio

Let the number of boys be 11x and the number of girls be 13x.

Step 2: Calculate the new number of boys and girls after 4 boys and 8 girls join the class

New number of boys = 11x + 4

New number of girls = 13x + 8

Step 3: Set up the equation based on the new ratio

Given the new ratio is 4:5, we can write the equation as:

(11x + 4) / (13x + 8) = 4/5

Step 4: Solve the equation

Cross-multiplying gives us:

5(11x + 4) = 4(13x + 8)

55x + 20 = 52x + 32

55x - 52x = 32 - 20

3x = 12

x = 4

Step 5: Calculate the strength of the class

Strength of the class = Initial number of boys + Initial number of girls + New boys + New girls

= 11x + 13x + 4 + 8

= 24x + 12

= 24*4 + 12

= 96 + 12

= 108

Explanation

Step 1: Understand the meaning

We are given two ratios and asked to find a common multiple — that is, a set of values for M, N, and O that fits both ratios proportionally.

Given Ratios:

1. M : N : O = 2 : 3 : 5

2. M : N : O = 4 : 5 : 6

We want to find a new ratio X : Y : Z that is proportional to both these given ratios.

Step 2: Check Option B: 8:15:30

Try simplifying 8:15:30:

Divide all terms by 1 (GCD is 1, so already simplified):
Still 8:15:30

Now check if it fits the first ratio (2:3:5):

• 8 ÷ 2 = 4

• 15 ÷ 3 = 5

• 30 ÷ 5 = 6

So 8:15:30 = 2×4: 3×5: 5×6 = 2:3:5 scaled up by different amounts?
No — wait! Those aren’t consistent scalings.

Instead, let’s try another way:

Divide 8:15:30 by 4:

• 8 ÷ 4 = 2

• 15 ÷ 5 = 3

• 30 ÷ 6 = 5

So 8:15:30 → 2:3:5  (matches first ratio)

Now divide 8:15:30 by 2:

• 8 ÷ 2 = 4

• 15 ÷ 3 = 5

• 30 ÷ 5 = 6

So 8:15:30 → 4:5:6  (matches second ratio)

8:15:30 is a common multiple of both 2:3:5 and 4:5:6

Explanation

⇒ Number of girls = 20

⇒ Number of boys = 15

The ratio of girls to boys: ⇒ Girls: Boys = 20:15

⇒ Girls: Boys = 20 ÷ 5: 15 ÷ 5 ⇒ Girls: Boys = 4:3

Explanation

To express 27 minutes 30 seconds and 1 hour in ratio:

Step 1: Convert both times to seconds

27 minutes 30 seconds = (27 * 60) + 30

= 1620 + 30

= 1650 seconds

1 hour = 60 minutes = 60 * 60

= 3600 seconds

Step 2: Calculate the ratio

Ratio = 1650 : 3600

To simplify, divide both parts by their greatest common divisor, which is 150:

= (1650 / 150) : (3600 / 150)

= 11 : 24

Explanation

Ratio of boys to girls = 3:2

Total students = 60

Total parts = 3 + 2 = 5

Number of girls = (2/5) × 60 = 24

Explanation

Let the two numbers be 5x and 6x, where x is their HCF.

Step 1: Calculate the LCM

The LCM of 5x and 6x is 30x.

Step 2: Find x

Given that the LCM is 480, we can set up the equation:

30x = 480

x = 480 / 30

x = 16

Explanation

1 hour = 60 minutes, so the ratio of an hour to a minute is 60 : 1.

It compares the larger unit (hour) to the smaller unit (minute).

Explanation

Let's denote the numbers as 8x and 3x.

Given: 8x - 3x = 20

5x = 20

x = 4

Step 1: Find the numbers

First number = 8x = 8 * 4 = 32

Second number = 3x = 3 * 4 = 12

Step 2: Find the sum

Sum = 32 + 12 = 44

Last updated by NA on 24-April-2026