Question 1

A sum of ₹ 7000 is divided among A, B, and C in such a way that the shares of A and B are in the ratio 2 : 3 and those of B and C are in the ratio 4 : 5, The ahare of B is

Accepted Answer

Given, A : B = 2 : 3 and B : C = 4 : 5 Then, A : B : C = 8 : 12 : 15 7there4; Share of B = [12/(8 + 12 + 15)] x 7000 = (12 x 7000)/35 = 2400 = ₹ 2400

Question 2

A sum of money is divided among A, B, C and D in the ratio of 3 : 7 : 9 : 13 . If the share of B is ₹, then what will be the total amount of money of A and C together?

Accepted Answer

Let A's share = 3N B's share = 9N and D's share = 13N According to the question 7N = 4872 ∴ N = 4872/7 = 696 Share of A and C = 3N + 9N = 12N = 12 x 696 = ₹ 8352

Question 3

The ratio between the ages of A and B is 3 : 5 and the sum of their ages is 56 yr. The ratio between their ages 7 yr ago was

Accepted Answer

Age of A = (3/8) x 56 = 21 yr Age of B = (5/8) x 56 = 35 yr Before 7yr, ration of the ages of A and B = (21 - 7) : (35 - 7) = 14 : 28 = 1 : 2

Question 4

The ratio of the ages of a father to that of their ages (in years) is 1000, then find the father's age after 10 yr.

Accepted Answer

Let the age of father = 5k and the age of son = 2k According to the question, 5k x 2k = 1000 ⇒ 10k2 = 1000 ⇒ k2 = 100 ∴ k = √100 = 10 ∴ Father's age after 10 yr = (5k + 10) = 5 x 10 + 10 = 60 yr

Question 5

35% of a number is two times 75% of another number. What is the ratio between the first and the second number, respectively?

Accepted Answer

Let first number is P and second number is Q. Then, according to the question, P x 35% = 2 x Q x 75% ⇒ (P x 35)/100 = (2 x Q x 75)/100 ⇒ P/Q = (2 x 75)/35 = (2 x 15)/7 = 30/7 ∴ P : Q = 30 : 7

Question 6

The ratio of milk and water in 85 kg of adulterated milk is 27 : 7. The amount of water which must be added to make the ratio 3 : 1 is?

Accepted Answer

Milk = 85 x (27/34) kg = 135/2 kg = 67.5 kg Water = 85 x (7/34) kg = 35/2 kg = 17.5 kg Let Amount of water to be added is x, ∵ 67.5 / (17.5 + x) = 3/1 ⇒ 3 (17.5 + x) = 67.5 ∴ x =5 ∴ Water to be added = 5 kg.

Question 7

Rs. 1870 has been divided into three parts in such away that half of the first parts, one-third of the second parts, and one-sixth of the third parts are equals. The third parts is?

Accepted Answer

1/2A = 1/3B =1/6C = x ⇒ A = 2x, B = 3x, C =6x ∴ A : B : C = 2 : 3 : 6 Third part = Rs. (1870 x 6/11) = Rs. 1020

Question 8

In a town 80% of the population are adults of which the men and women are in the ratio of 9 : 7, respectively. If the number of adult women is 4.2 lakh, what is the total population of the town?

Accepted Answer

let the number of adult men be N. Then, ratio of the numbers of adult men and adult women 9 : 7 = N : 4.2 ⇒ N = (9/7) x 4.2 = 5.4 Lakh Total adult population = 4.2 + 5.4 = 9.6 lakh. If the population of the town be M Lakh, then, 80M/100 = 9.6 ⇒ M = (9.6 x 100)/80 = 12 lakh

Question 9

Mr. Shrimant inherits 2505 gold coins and divides them among his three sons, Bharat, Parat and Marat, in a certain ratio. Out of the total coins received by each of them, Bharat sells 30 coins Parat donates his 30 coins and Marat losses 25 coins. No…

Accepted Answer

According to the question. (46k +30) + (41k + 30) + (34k + 25) = 2505 ⇒ 121k = 2505 - 85 = 2420 ∴ k = 2420/121 = 20 ∴ Number of coins received by Parat = 41k + 30 = 41 x 20 + 30 = 850

Question 10

₹ 600 are divided among A, B and C such that ₹ 40 more then 2/5th of A's share, ₹ 20 more then 2/7 th of B's Share and ₹ 10 more then 9/17 th of C's share, all are equal. What is B's share?

Accepted Answer

2A/5 + 40 = 2B/7 + 20 = 9C/17 + 10 = K Then, A = (5/2) x (K - 40), B = (7/2) x (K - 20), C = (17/9) x (K - 10) According to the question, A + B + C = 600 ⇒ (5/2) x ( K - 40) + (7/2) x (K - 20) + (17/9) x (K - 10) = 600 ⇒ 45 x (K - 40 ) + 63 x (K - 20) + 34 x (K - 10) = 10800 ⇒ 45K - 1800 + 63K - 1260 + 34K - 340 = 10800 ⇒ 142K - 3400 = 10800 ⇒ 142K = 10800 + 3400 ⇒ 142K = 14200 ∴ K = 14200/142 =100 ∴ B = (7/2) x (K - 20) = (7/2) x (100 - 20) = (7 x 80)/2 = 7 x 40 = ₹ 280

Question 11

Salaries of Akash, Bablu and Chintu are in the ratio of 2 : 3 : 5. If their salaries were increased by 15%, 10% and 20% respectively, then what will be the new ratio of their salaries?

Accepted Answer

Ratio of salaries Akash : Babloo : Cintu 2 : 3 : 5 Let the common ratio be 'k' Then, salaries of Akash, Babloo and chintu will be 2k, 3k and 5k, respectively. Now, 15% increase in Akash's salary = 15% of 2k = 15 x 2k/100 = 0.3k New salary = 2k + 0.3k = 2.3k Also, 10% increase in Babloo's salary = 10% of 3k = 10 x 3k/100 = 0.3k ∴ New salary = 3k + 0.3k = 3.3k Again, 20%increase in Chintu's salary = 20% of 5k = 20 x 5k/100 = 1k New salary = 5k + k = 6k ∴ New ratio = Ratio of new salaries = 2.3k : 3.3k : 6k On multiplying with 10 and dividing by k ratio will be 23 : 33 : 60.

Question 12

In the month of January, Arun's income and expenses were ₹ 15000 and ₹ 9000, respectively. His monthly expenses vary directly as the square of his monthly income. What is his income when it just equals his expenses?

Accepted Answer

According to the question Expenses ∞ (income)2 ⇒ 9000 = K (15000 )2 ∴ K = 9000/(15000)2 = 1/25000 Again E = K x 12 ⇒ 1 = K x 12 [∴ exenses = income] ∴ 1 = 1/K = 25000 ∴ Required answer = ₹ 25000

Question 13

A cat takes 5 leaps for every 4 leaps of a a dog but 3 leaps of the dog are equal to 4 leaps of the cat. What is the ratio of the speeds of the cat to that of the dog?

Accepted Answer

4 leaps of cat = 3 leaps of dog ⇒ 1 leap of cat = 3/4 leap dog Cat takes 5 leaps for every 4 leaps of dog ∴ Required ratio = (5 x Cat's leap ) : ( 4 x Dog's leap) = (5 x 3/4 dog's leap) : (4 x Dog's leap) = 15 : 16

Question 14

The respective ratio of Sita's Riya's and Kunal's monthly incomes is 84 : 76 : 89. If riya's annual income ₹ 456000, then what is the sum of Sita and Kunal's annual incomes? (In some cases monthly income and in some cases annual income is used).?

Accepted Answer

Let monthly income of Sita Riya and Kunal be 84k, 76k and 89k, respectively. Given annual income of Riya = 456000 ∴ Monthly income of Riya = 456000/12 = 38000 ∴ 76k = 38000 ⇒ k = 500 So, the monthly income of Sita and Kunal = 84k + 89k = 173k = 173 x 500 = 86500 Therefore, annual income = 86500 x 12 = ₹ 1038000

Question 15

₹ 2186 are distributed among A, B and C . If money given to them is decreased by ₹ 26, ₹ 28 and ₹ 32 respectively, then they have money in the ratio of 9 :13 : 8. What is the amount given to A?

Accepted Answer

Amount given to A= 9k + 26 Amount given to B = 13k + 28 and amount given to C = 8k + 32 According to the question, (9k + 26) + (13k + 28) + (8k + 32) = 2186 ⇒ 30 k + 86 = 2186 ⇒ 30 k = 2100 ∴ k = 70 Hence, amount given to A = 9k + 26 = 9 x 70 + 26 = 630 + 26 = ₹ 656

Question 16

A person gave 2/5 part of his income to his elder son and 30 % part to his younger son. He saved his remaining money in three trusts. A, B and C in the ratio of 3 : 5 : 2. If difference between the amount got by his both sons is &8377; 2000, How muc…

Accepted Answer

Let the person have ₹ N Then shares of elder don = ₹ 2N/5 and share of younger son = ₹ 3N/10 According to the question, 2N/5 - 3N/10 = 2000 ⇒ N/10 = 2000 ⇒ N = 20000 Remaining amount saved in trusts = 1 - (2N/5 + 3N/10 ) = 1 - (4N + 3N)/10 = 1 - 7N/10 = 3N/10 x 20000 = 6000 given that A : B : C = 3 : 5: 2 ∴ Share of C = [2/(3 + 5 +2)] x 6000 = (2/10) x 6000 = ₹ 1200

Question 17

In a factory the ratio of the number of employee of three types A, B and C is 9 : 13 : 18 and their wages are in the ratio of 10 : 7 : 4. If number of employees of type C is 54 and wages of every employee of type 54 and wages of every employee of ty…

Accepted Answer

Given ratio of employee = 9 : 13 : 18 Let number of A's emplouees = 9k Number of B's employees = 13k and number of C's employees = 18k According to the question 18k = 54 ∴ k = 3 ∴ Number of employee of type A = 9 x 3 = 27 Similarly, Wages of every employee of types A = 10/7 x 1400 = ₹ 2000 Required wages = 27 x 2000 = ₹ 54000

Question 18

Brothers A and B had some savings in the ratio 4 : 5. They decided to buy a gift for their sister, sharing the cost in the ratio 3 : 4. After they bought, A spent two-third of his amount, while B is left with ₹ 145. Then, the value of the gift is

Accepted Answer

Let the saving of A and B are 4p, 5p and the share in cost of gift are 3q, 4q respectively. According to the question, For A, 4p - 3q = (2/3) x 4p ⇒ p = 9q/4 ..... (i) For B, 5p - 4q = 145 ⇒ 5 x (9q/4) - 4q = 145 .....[by Eq. (ii) ∴ q = 20 ∴ Cost of gift = 3q + 4q = 7 x 20 = ₹ 140

Question 19

The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ratio of the number of boys to the number of girls in the class is:-

Accepted Answer

Let the ratio be x : y Total boys = 16.4 X x Total girls = 15.4 X y Total number of students in class = 16.4x + 15.4y The average age of all students is 15.8 The total age of boys is 15.8x The total age of girls is 15.8y 16.4x + 15.4y = 15.8x + 15.8y 0.6 x = 0.4 y x/y = 0.4/0.6 = 2/3

Ratio and Proportion Questions