Question 1

Divide Rs.6500 among A, B and C so that after spending 90%, 75% and 60% of their respective saving was in the ratio of 3: 5: 6

Accepted Answer

A's spending 90% therefore saving = 10% B's spending 75% therefore saving = 25% C's spending 60% therefore saving = 40% Let us suppose A, B and C saves Rs. 3, 5 and 6 respectively. 10% of A's saving = Rs. 3 100% of A's saving = (3/10)*100 = Rs. 30 25% of B's saving = Rs. 5 100% of B's saving = (5/25)*100 = Rs. 20 40% of C's saving = Rs.6 100% of C's saving = (6/40)*100 = Rs. 15 Divide Rs. 6500 in the ratio of 30 : 20 : 15 A's Share = (30/65)*6500 = Rs. 3000 B's Share = (20/65)*6500 = Rs. 2000 C's Share = (15/65)*6500 = Rs. 1500

Question 2

The ratio of male and female in a city is 7 : 8 respectively and percentage of children among male and female is 25 and 20 respectively. If number of adult females is 156800, what is the total population of the city?

Accepted Answer

Let the total population be 'p' Given ratio of male and female in a city is 7 : 8 In that percentage of children among male and female is 25% and 20% => Adults male and female % = 75% & 80% But given adult females is = 156800 => 80%(8p/15) = 156800 => 80 x 8p/15 x 100 = 156800 => p = 156800 x 15 x 100/80 x 8 => p = 367500 Therefore, the total population of the city = p = 367500

Question 3

The third proportional to x2-y2 and x-y is :

Accepted Answer

Let the third proportional to x 2 - y 2 and x - y be z. Then, x 2 - y 2 : x - y : : x - y : z = > x 2 - y 2 * z = x - y 2 => z= x - y 2 x 2 - y 2 = x - y x + y

Question 4

If 76 is divided into four parts proportional to 7, 5, 3, 4, then the smallest part is:

Accepted Answer

Given ratio = 7 : 5 : 3 : 4, Sum of ratio terms = 19. Smallest part = (76*3/19) = 12

Question 5

The wages of labourers in a factory increases in the ratio 22:25 and there was a reduction in the number of labourers in the ratio 15:11. Find the original wage bill if the present bill is Rs. 5000 ?

Accepted Answer

The wages of labourers in a factory increases in the ratio 22:25 and there was a reduction in the number of labourers in the ratio 15:11. Find the original wage bill if the present bill is Rs 5000 ? Ratio of increase of wages = 22:25 Ratio of decrease of labourers = 15:11 Compound ratio of wages of labourers = 22 x 15 : 25 x 11 = 330:275 Final bill = Rs. 5000 For 275 ratio wages = Rs. 5000 For 1 ratio wages = 5000/275 For 330 ratio wages = 5000/275 x 330 = Rs. 6000

Question 6

3 : 12 :: 5 : ?

Accepted Answer

3 3 2 + 3 = 12 5 5 2 + 5 = 30

Question 7

One year ago the ratio between Maneela’s and Shanthi’s salary was 3 : 4. The ratios of their individual salaries between last year’s and this year’s salaries are 4 : 5 and 2 : 3 respectively. At present the total of their salary is Rs. 4160. The sal…

Accepted Answer

Let the salaries of Maneela and Shanthi one year before be M1, S1 & now be M2, S2 respectively. Then, from the given data, M1/S1 = 3/4 .....(1) M1/M2 = 4/5 .....(2) S1/S2 = 2/3 .....(3) and M2 + S2 = 4160 .....(4) Solving all these eqtns, we get M2 = Rs. 1600.

Question 8

For any two numbers m , n ; (m+n) : (m-n) : mn = 7: 1: 60 . Find the value of 1/m : 1/n

Accepted Answer

m + n m - n = 7 x x ⇒ m n = 4 x 3 x Again m n = 12 x 2 and mn =60x so, 60 x = 12 x 2 ⇒ x = 5 => m= 20 and n= 15 Hence, 1 m : 1 n = 1 20 : 1 15 = 3 : 4

Question 9

A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long?

Accepted Answer

If you double the sides of a cube, the ratio of the surface areas of the old and new cubes will be 1: 4. The ratio of the volumes of the old and new cubes will be 1: 8. Weight is proportional to volume. So, If the first weighs 6 pounds, the second weighs 6x8 pounds =48.

Question 10

Rice worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, then the price of third variety of rice per kg?

Accepted Answer

Let the price of required variety = Rs. P/kg Then, respective amounts were m kg, m kg and 2m kg = 126m + 135m + 2pm = 153 x 4m => 2p = 351 p = 175.5 / kg

Question 11

If the ratio of the ages of two friends A and B is in the ratio 3 : 5 and that of B and C is 3 : 5 and the sum of their ages is 147, then how old is B?

Accepted Answer

The ratio of the ages of A and B is 3 : 5. The ratio of the ages of B and C is 3 : 5. B's age is the common link to both these ratio. Therefore, if we make the numerical value of the ratio of B's age in both the ratios same, then we can compare the ages of all 3 in a single ratio. The can be done by getting the value of B in both ratios to be the LCM of 3 and 5 i.e., 15. The first ratio between A and B will therefore be 9 : 15 and the second ratio between B and C will be 15 : 25. Now combining the two ratios, we get A : B : C = 9 : 15 : 25. Let their ages be 9x, 15x and 25x. Then, the sum of their ages will be 9x + 15x + 25x = 49x The question states that the sum of their ages is 147. i.e., 49x = 147 or x = 3. Therefore, B's age = 15x = 15*3 = 45

Question 12

The ratio of the incomes of Pavan and Amar is 4 : 3 and the ratio of their expenditures are 3:2. If each person saves Rs. 1889, then find the income of Pavan?

Accepted Answer

Let ratio of the incomes of Pavan and Amar be 4x and 3x and Ratio of their expenditures be 3y and 2y 4x - 3y = 1889 ......... I and 3x - 2y = 1889 ...........II I and II y = 1889 and x = 1889 Pavan's income = 7556

Question 13

Three cats are roaming in a zoo n such a way that when cat A takes 5 steps, B takes 6 steps and C takes 7 steps.But the 6 steps of A are equal to the 7 steps of B and 8 steps of C. what is the ratio of their speeds?

Accepted Answer

Frequency of step of A:B:C = 5 : 6 : 7 But in terms of size of step, 6A = 7B = 8C Therefore, Ratio of speeds of A, B and C = 5/6 : 6/7 : 7/8 = 140 : 144 : 147

Question 14

A child has three different kinds of chocolates costing Rs.2, Rs.5, Rs.10. He spends total Rs. 120 on the chocolates. what is the minimum possible number of chocolates he can buy, if there must be atleast one chocolate of each kind?

Accepted Answer

Minimum number of chocolates are possible when he purchases maximum number of costliest chocolates. Thus, 2 x 5 + 5 x 2 =Rs.20 Now Rs.100 must be spend on 10 chocolates as 100 = 10 x 10. Thus minumum number of chocolates = 5 + 2 + 10 = 17

Question 15

The ratio of Pens and Pencils in a shop is 3 : 2 respectively. The average number of Pens and Pencils is 180. What is the number of Pencils in the shop?

Accepted Answer

Given ratio of pens and pencils = 3 :2 Number of Pens = 3x Number of Pencils = 2x Average number of pencils & Pens = 3 x + 2 x 2 = 180 5x = 360 => x = 72 Hence, the number of pencils = 2x = 72 x 2 = 144.

Question 16

Two numbers are in the ratio 3 : 7. If 6 be added to each of them, then they are in the ratio 5 : 9. Find the numbers ?

Accepted Answer

Let the two numbers be x and y Given x : y = 3 : 7 .....(1) Now, x+6 : y+6 = 5 : 9 .....(2) From (1), x = 3y/7 From (2), 5y - 9x = 24 => 5y - 9(3y/7) = 24 => y = 21 => From(1), x = 9 Hence, the two numbers be 9 and 21

Question 17

Vinod have 20 rupees. He bought 1, 2, 5 rupee stamps. They are different in numbers by the reason of no change, the shop keeper gives 3 one rupee stamps. So how many stamps Vinod have ?

Accepted Answer

Given total rupees = 20 Rs No. of one rupee stamps = 3 Now, remaining money = Rs. 17 With that he buys only 2 and 5 rupee stamps Let number of Rs. 5 stamps = K Let number of Rs. 2 stamps = L 5K + 2L = 17 K = 3, L = 1 (possible) L = 6, K = 1 (possible) => But given that they are different in number so, K is not equal to 3 one rupee stamps = 3 2 two stamps = 6 5 rupee stamps = 1 Total number of stamps = 10.

Question 18

The incomes of two persons A and B are in the ratio 3 : 4. If each saves Rs.100 per month, the ratio of their expenditures is Rs. 1 : 2. Find their incomes.

Accepted Answer

Let the incomes of A and B be 3P and 4P. If each saves Rs. 100 per month, then their expenditures = Income - savings = (3P - 100) and (4P - 100). The ratio of their expenditures is given as 1 : 2. Therefor, (3P - 100) : (4P - 100) = 1 : 2 Solving, We get P = 50. Substitute this value of P in 3P and 4P. Thus, their incomes are : Rs.150 and Rs.200

Question 19

In a competitive exam, the number of passed students was four times the number of failed students. If there had been 35 fewer appeared students and 9 more had failed, the ratio of passed and failed students would have been 2 : 1, then the total numb…

Accepted Answer

Let the number of failed students be x => Number of passed students = 4x So total number of students was 5x From the given data, If total number of students be 5x – 35 => 4x-35-9/x+9 = 2/1 => 4x – 44 = 2(x + 9) => 4x – 2x = 18 + 44 => x = 31 Total number = 31×5 = 155

Ratio and Proportion Questions