Ratio and Proportion 2
The ratio of the number of boys and girls in a college is 7: 8. If the percentage increase in the number of boys and girls be 20% and 10 % respectively, what will be the new ratio?
Originally, let the number of boys and girls in the college be 7x and 8x respectively.
Their increased number is (120% of 7x) and (110% of 8x)
∴ Required ratio
=
In what proportion must a number be divided so that ¼ of the first part and ⅓ of the second part are together equal to ½ of the original number?
Let number be divided in ratio x : y. Then
First part ,
second part
Now,
Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 28.8 kg of zinc has been consumed in it?
For 9 kg zinc, mixture melted = (9 + 11) kg.
For 28.8 kg zinc, mixture melted
The Binary Ice-cream Shopper sells two flavours : Vanilla and Chocolate. On Friday, the ratio of Vanilla cones sold to Chocolate cones sold was 2 : 3. If the store had sold 4 more Vanilla cones, then, the ratio of Vanilla cones sold to the Chocolate cones sold would have been 3 : 4. How many Vanilla cones did the store sell on Friday?
and …(1)
∴ C =
⇒ [From (1)]
where V denoted for vanilla and C for chocolate.
⇒ 4V + 16 =
⇒ 8V + 32 = 9V
⇒ V = 32
The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is:
A : B = 2 : 3 = 2 × 5 : 3 × 5 = 10 : 15
and B : C = 5 : 8 = 5 × 3 : 8 × 3 = 15 : 24
Therefore, A : B : C = 10 : 15 : 24
Let the numbers be 10x, 15x and 24x.
Then, 10x + 15x + 24x = 98
⇒ 49x = 98
⇒ x = 2
⇒ Second number = 15x = 15 × 2 = 30
The ratio of number of ladies to gents at a party was 1 : 2, but when 2 ladies and 2 gents left, the ratio became 1 : 3. How many people were originally present at the party?
Let number of ladies = x
and, number of gents = 2x
⇒ x = 4
∴ Total number of people originally present = 4 + 8 = 12
A man divides his property so that his son’s share to his wife’s and the wife’s share to his daughter are both in the ratio 3 : 1. If the daughter gets ₹10,000 less than the son, find the total worth of the property.
Let Son’s share = ₹S;
Daughter’s share = ₹D;
and Wife’s share = ₹W.
Also, S : W = W : D = 3 : 1
∴ S : W : D = 9 : 3 : 1
then S = 9x , D = x
and 9x – x = 10,000
⇒ x = ₹1250
∴ Total worth of the property
= (9 + 3 + 1) x = 13x
= 13 × 1250 = ₹16,250
Mrs X spends ₹535 in purchasing some shirts and ties for her husband. If shirts cost ₹43 each and the ties cost ₹21 each, then what is the ratio of the shirts to the ties, that are purchased?
Let S denotes the shirts and T denotes the ties.
We have, 43S + 21T = 535
By hit and trial, S = 10, T = 5
⇒ 43 × 10 + 21 × 5 = 535
∴ Ratio of shirts to ties = 10 : 5 = 2 : 1
The ratio between the number of passengers travelling by I and II class between the two railway stations is 1 : 50, whereas the ratio of I and II class fares between the same stations is 3 : 1. If on a particular day, ₹1325 revenue collected from the passengers travelling between these stations, then what was the amount collected from the II class passengers?
Let, the number of passengers travelling by I and II class be x and 50x and fares of I and II class be 3y and y.
∴ Revenue is x × 3y + 50x × y = ₹1325
53xy = 1325
⇒ xy = 25
∴ Amount collected from the II class passengers
= 50xy
= 50 × 25
= ₹1250.
Railway fares of 1st, 2nd and 3rd classes between two stations were in the ratio of 8 : 6 : 3. The fares of 1st and 2nd class were subsequently reduced by 1/6 and 1/12, respectively. If during a year, the ratio between the passengers of 1st, 2nd and 3rd classes was 9 : 12 : 26 and total amount collected by the sale of tickets was ₹1088, then find the collection from the passengers of 1st, class.
Fare after reduction.
Ratio of revenue
Ratio of revenue of all three classes
= 10 : 11 : 13
∴ Collection for 1st class
The income of A and B are in the ratio 3 : 2 and expenses are in the ratio 5 : 3. If both save ₹200, what is the income of A?
Let income of A = ₹3x,
income of B = ₹2x
and expenditure of A = ₹5y,
expenditure of B = ₹3y
Now, saving = income – expenditure
∴ 3x – 5y = 2x – 3y = 200
⇒ x = 2y and y = 200
∴ x = 400
∴ A’s income = ₹1200
A sum of money is divided among A, B and C in the ratio of 3¾ : 4 : 5.5. If the lowest share is ₹30, then the total amount of money is
Let A’s share ,
B’s share = ₹4x and
C’s share = ₹5.5x
Given
∴ Total amount = 30 + 32 + 44 = ₹106
At a start of a seminar, the ratio of the number of male participants to the number of female participants was 3 : 1. During the tea break 16 participants left and 6 more female participants registered. The ratio of the male to the female participants now became 2 : 1. What was the total number of participants at the start of the seminar?
Let the number of male and female participants be 3x and x respectively.
therefore total no. of participants are 4x.
During the tea break, the number of male participants are
... (i)
and the number of female participants are
... (ii)
⇒ 3x – 12 = 2x + 4
⇒ x = 16
Therefore, the total number of participants = 4 × 16 = 64.
The ratio of the present ages of Sushma and Karishma is 6:7 respectively. The ratio of their ages 8 years hence would be 8:9 respectively. What would be the respective ratio of their ages after 12 years?
Let the present ages of Sushama and Karishma be 6x and 7x respectively.
∴
or 56x + 64 = 54x + 72
Required ratio
= 9 : 10
The ratio of the present ages of Smita and Kavita is 3:8 respectively. Seven years hence the respective ratio of their ages will be 4:9. What is Kavita’s present age?
Let the present ages of Smita and Kavita be 3x and 8x years respectively
According to questions,
⇒ 32 x + 28 = 27x + 63
⇒ 32x – 27x = 63 – 28
⇒ 5x = 35
⇒ x = = 7
∴ Kavita’s present age = 8x = 8 × 7 = 56 years
The average age of a man and his son is 48 years. The ratio of their ages is 5 : 3 respectively. What is the son’s age?
Let the ages of man and his son be 5x and 3x respectively.
5x + 3x = 2 × 48
⇒ 8x = 96
⇒ x = = 12
∴ Son’s age = 12 × 3 = 36 years
The ages of Nishi and Vinnee are in the ratio of 6 : 5 respectively. After 9 years the ratio of their ages will be 9 : 8. What is the difference in their ages?
Difference in age
= 3 years
The difference between the present ages of Arun and Deepak is 14 years. Seven years ago the ratio of their ages was 5 : 7 respectively. What is Deepak’s present age?
Let Arun’s present age be x years.
Then, Deepak’s present age = (x + 14) years
Then,
⇒ 7x – 5x = 35 + 49
∴ Deepak’s present age
= 42 + 14 = 56 years
At present Meena is eight times her daughter’s age. Eight years from now, the ratio of the ages of Meena and her daughter will be 10 : 3 respectively. What is Meena’s present age?
Present age of Meena
= 32 years
The ratio of the ages of a father and son is 17 : 7 respectively. 6 years ago the ratio of their ages was 3 : 1 respectively. What is the father’s present age?
Let the present age of father and son be 17x and 7x respectively.
⇒ 21x – 17x = 18 – 6
⇒ x = 12 ÷ 4 =3
∴ Father’s present age
= 17 × 3 = 51 years.
The respective ratio of the present ages of Swati and Trupti is 4: 5. Six years hence the respective ratio of their ages will be 6 : 7. What is the difference between their ages?
Let the present ages be 4x and 5x respectively.
⇒ 30x – 28x = 42 – 36
⇒ x = ⁶⁄₂ = 3
∴ Difference in age
= 5x – 4x = x = 3 years
The average age of three boys is 25 years and their ages are in the proportion 3: 5 : 7. The age of the youngest boy is:
Total age of 3 boys
= (25 × 3) years
= 75 years
Ratio of their ages = 3 : 5 : 7.
Age of the youngest boy
= years
= 15 years
A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is ₹35, how many coins of each type are there?
Let number of each type of coin = x. Then,
1 × x + 0.50 × x + 0.25 x = 35
⇒ 1.75x = 35
⇒ x = 20 coins
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