Explanation

Ratio of boys to girls = 5:3

If 5 parts = 40 boys, then 1 part = 40 ÷ 5 = 8

Girls = 3 parts = 8 × 3 = 24 girls.

Explanation

Given a : b : c = 3 : 4 : 7.

Let's find (a + b + c) : c or any other single term. Here we find (a + b + c) : a

a + b + c = 3 + 4 + 7 = 14

(a + b + c) : a = 14 : 3

Explanation

We are given:

• 12 men + 16 boys complete the work in 5 days

• 13 men + 24 boys complete the work in 4 days

• We need to find the ratio of the daily work done by a man to that of a boy.

Step 1: Let M be work done by 1 man in 1 day and B be work done by 1 boy in 1 day

5(12M+16B)=1

4(13M+24B)=1

Step 2: Convert to equations

12M+16B=⅕

4(13M + 24B) = 1​

Step 3: Solve for M and B

Multiply first equation by 4:

48M+64B=⅘

Multiply second equation by 5:

65M+120B=5/4

Convert fractions:

4/5=0.8,5/4=1.25

Solving simultaneously:

Using elimination: Multiply (48M + 64B = 0.8) by 5:

240M+320B=4240M + 320B = 4240M+320B=4

Multiply (65M + 120B = 1.25) by 4:

(260M+480B)- (240M + 320B) =5-4

20M + 160 b = 1

Dividing by 20:

M+8B=1/20M 

Substituting M = 2B from Question 69:

2B+8B=1/20

10B=20/1​

 B=1/200B

​ M=2×1/200=2/200=1/100M

Thus, ratio M:B = 2:1.

Explanation

Let the amount be divided into 7x,4x,3x and 2x.

7x-2x = 500 5x=500 x = 100

Total amount = 7x+4x+3x+2x = 16x = Rs.1600

Explanation

Given x:y = 3:4 and y:z = 2:5.

To find x:z, we need to make y's ratio the same in both.

y:z = 2:5 = 4:10 (multiply both parts by 2)

Now, x:y = 3:4 and y:z = 4:10

So, x:z = 3:10.

Explanation

To find the fourth proportional, we need to set up a proportion:

60 : 48 :: 30 : x

Where x is the fourth proportional.

We can rewrite this as: 60/48 = 30/x

Cross-multiplying, we get: 60x = 30 × 48

Simplifying, we get: 60x = 1440

Dividing both sides by 60, we get: x = 24

So, the fourth proportional is 24.

Explanation

Let's assume 2/3 A = 3/4 B = 0.6C = 18

2/3 A = 18 ⇒ A = 27

3/4 B = 18 ⇒ B = 24

0.6C = 18 ⇒ C = 30

A:B:C = 27:24:30 = 9:8:10

Explanation

Explanation

1. 3/4 of the students do not know either Hindi or English.

This means that 1 - 3/4 = 1/4 of the students know either Hindi or English or both.

2. 1/6 of the students know English.

3. 1/8 of the students know Hindi.

Now, let's use the principle of inclusion-exclusion:

Number of students who know either Hindi or English or both = Number of students who know English + Number of students who know Hindi - Number of students who know both

We know that 1/4 of the students know either Hindi or English or both. We also know the number of students who know English (1/6) and the number of students who know Hindi (1/8).

Let x be the number of students who know both English and Hindi.

Then, we can set up the equation:

1/4 = 1/6 + 1/8 - x

Combine like terms:

1/4 = 7/24 - x

Add x to both sides:

x = 7/24 - 1/4

x = 7/24 - 6/24

x = 1/24

So, 1/24 of the students know both English and Hindi.

Explanation

Let's denote the number of coins as 2x, 3x, and 4x for Rs 2, Rs 5, and Rs 10 coins, respectively.

The total value is:

2(2x) + 5(3x) + 10(4x) = 472

4x + 15x + 40x = 472

59x = 472

x = 8

Number of Rs 2 coins = 2x = 2(8) = 16