Given:

Initially the ratio of number of students = 2 : 3 : 4

After adding 12 students in each class, the ratio becomes = 8 : 11 : 14

Calculation:

Let number of students in each class be 2x, 3x and 4x respectively.

After adding 12 students in each class, the number of students becomes 2x + 12, 3x + 12, 4x + 12

After adding 12 students in each class, the ratio becomes = 8 : 11 : 14

So, equating the ratio of first two classes:

2x + 12 : 3x + 12 = 8 : 11

2x + 12 / 3x + 12 = 8 / 11

22x + 132 = 24x + 96

2x = 36

x = 18

So, we get the number of students in each class before adding 12 students as:

2x = 2 × 18 = 36

3x = 3 × 18 = 54

4x = 4 × 18 = 72

So, the total number of students before adding 12 students in each class = 2x + 3x + 4x = 9x = 9 × 18 = 162

Hence, option 1 is correct.

Given:

Total amount=1320 rupees

There are 7 men, 11 women and 5 boys.

Calculation:

Let share of each man, woman and boy be x, y and z respectively.

Total share of 7 men, 11 women and 5 boys=7x + 11y + 5z = 1320 rupees  ---------(1.)

It is given that share of a woman is 3 times that of a boy, i.e. y = 3z   ---------(2.)

It is given that a man receives a sum equal to the share of a woman and a boy i.e. x = y + z  ---------(3.)

Putting equation 2 in equation 3, we get,

x = 3z + z = 4z ---------(4.)

Putting equation 4 and equation 2 in equation 1, we get,

7 × 4z + 11 × 3z + 5z = 1320

28z + 33z + 5z = 1320

66z = 1320

z = 20

Putting value of z in equation 4, we get value of x,

x = 4z = 4 × 20 = 80

Putting value of z in equation 2, we get value of y,

y = 3z = 3 × 20 = 60

The shares of each man, woman and boy are 80, 60 and 20 respectively.

Hence, option 1 is correct. 

Given:

The sum of three nos. J, O and Y is 118.

The ratio between J and O is 3 : 4.

The ratio between O and Y is 5 : 6.

Formula Used:

Simple concept of Ratio.

Calculation:

It is given that, J + O + Y = 118       ----(1)

And, J/O = 3/4

⇒ J = (3 × O)/4

Also, O/Y = 5/6

⇒ Y = (6 × O)/5

Put the values of J and Y in eq. (1)

(3 × O)/4 + O + (6 × O)/5 = 118

⇒ (59/20) × O = 118

⇒ O = 118 × 20 / 59

⇒ O = 40

∴ The value of the second number O is 40.

Alternate Method

J : O = 3 : 4       ----(i)

O : Y = 5 : 6       ----(ii)

To make the value of O in both the ratios, We have to multiply 5 with equation (i) and 4 with equation (ii)

5 × (J : O) = 15 : 20

4 × (O : Y) = 20 : 24

So, J : O : Y = 15 : 20 : 24

Let J = 15x

O = 20x

Y = 24x

15x + 20x + 24x = 118

⇒ 59x = 118

⇒ x = 2

So, value of O = 20 × 2 = 40

∴ value of O is 40

Quantity of acid in the solution = 729 × 7/9 = 567 litres

Quantity of water in the solution = 729 - 567 = 162 litres

Let quantity of added water be x, then

⇒ 567/(162 + x) = 5/3

⇒ 3 × 567 = 5 × 162 + 5x

⇒ 1701 = 810 + 5x

⇒ 5x = 1701 - 810

⇒ x = 178.2

Given:

A ∶ B ∶ C = 3 : 9 : 13

Total amount = Rs. 2025

Calculation:

Let the share of A, B, and C be 13x, 9x and 3x respectively

Total share of A, B, and C = (13x + 9x + 3x) = 25x

Now, Total amount = Rs. 2025

So, 25x = 2025

⇒ x = 81

Difference between share of A and share of C = (13x – 3x) = 10x

So, 10x = 10 × 81 

⇒ Rs. 810

∴ Difference between share of A and share of C is Rs. 810

The ratio of boys and girls in a group is = 7x : 6x

According to the question

(7x + 4)/(6x – 3) = 4/3

⇒ 3 (7x + 4) = 4 (6x – 3)

⇒ 21x + 12 = 24x – 12

⇒ 24x – 21x = 12 + 12

⇒ 3x = 24

⇒ x = 24/3 = 8

∵ 8 year ago the ratio of age of father and his son was 7 : 4

Let the father and son age be 7x and 4x respectivily

Present age of father and son is (7x + 8) and (4x + 8) respectivily

According to question,

(7x + 8) + (4x + 8) = 126

⇒ 11x + 16 = 126

⇒ x = 10

Present age of father = (7x + 8) = 78 years and present age of son = (4x + 8) = 48 years

After 7 years, father = 78 + 7 = 85 years and son = 48 + 7 = 55 years

Given:

Total amount the man had = Rs. 8910

Ratio of shares between his three daughters Sakshi, Priya and Suhani = 7 : 11 : 9

Calculation:

Let the share of Sakshi, Priya and Suhani be 7x, 11x and 9x respectively

Total share of 3 daughters = (7x + 11x + 9x)

⇒ 27x

Now, difference between share of Priya and Suhani = 11x – 9x

⇒ 2x

Now, according to question

27x = Rs. 8910

⇒ 2x = (8910/27x) × 2x

⇒ Rs. (330 × 2)

⇒ Rs. 660

∴ The difference between share of Priya and Suhani is Rs. 660

Given:

The average weight of ring = 10 gm

Ring contains gold and copper in the ratio of 9.5 : 0.5

Calculation:

Ring contains gold and copper in the ratio of (9.5 : 0.5) × 2 = 19 : 1  ...........(Ratio multiplied with 2 to remove the decimal ratios)

if the ratio of gold and copper = 19 : 1, then Let the new wight of ring be 10 × 2 = 20 gm

20 gm of the ring contains 19 gram gold and 1 gram copper

Now, the weight of the new ring = 8 gm

The same ratio of gold and copper is to be maintained, i.e., 19 : 1

Weight of copper = [1/(19 + 1)] × 8 gm = 8/20 gm = 0.4 gram

Given:

The income of A and C = 7 ∶ 11

Sum of Income of A and C = 72,000/-

The income of B – Income of A = Income of C – Income of B

Concept:

The gap of income of A, B, C is equal, i.e, if A ∶ B ∶ C, then B – A = C – B.

Calculation:

Let the income of A = 7x

Income of C = 11x

∵ Income of (A + C) = 72,000/-

⇒ 7x + 11x = 72,000

⇒ 18x = 72,000

⇒ x = 72,000/18 = 4000

∴ Income of A = 7x = 7 × 4000 = 28,000/-

Income of C = 11x = 11 × 4000 = 44,000/-

∴ Income of B – 28,000 = 44,000 – Income of B

⇒ 2(Income of B) = 72,000/-

⇒ Income of B = 72,000/2 = 36,000/-