Question 1

729 ml of a mixture contains milk and water in the ratio 7 : 2. How much more water is to be added to get a new mixture containing milk and water in the ratio of 7 :3?

Accepted Answer

Milk = (729 x 7/9) = 567 ml Water = (729 x 2/9) = 162 ml Let water to be added is w ∵ 567 / (162 + w) = 7/3 ⇒ 3 x 567 - 7 x 162 = 7 x w ⇒ 1701 - 1134 = 7 x w ∴ 7w = 1701 - 1134 ∴ w = 567/7 = 81 ml

Question 2

A and B are two alloys of gold and copper prepared by mixing metals in proportions 7 : 2 and 7 : 11 respectively. If equal quantities of the alloys are melted to from a third alloy C, the proportion of gold and copper in C will be?

Accepted Answer

Gold in C =(7/9 + 7/18) = 21/18 = 7/6 Copper in C = (2/9 + 11/18) = 15/18 = 5/6 ∴ Gold : Copper = 7/6 : 5/6 = 7 : 5

Question 3

Some money is divided among A, B and C in such a way that 5 times A's share 3 times B's share and 2 times C's share are all equal. the ratio between the share of A, B, C is?

Accepted Answer

∵ 5A = 3B = 2C = x ⇒ A = x/5, B=x/3 and C =x/2 ∴ A : B : C = x/5 : x/3 : x/2 = 6 : 10 : 15

Question 4

94 is divided into two parts in such a way that fifth parts of the first and eighth parts of the second are in the ratio 3 : 4. The first parts is?

Accepted Answer

∵ 1/5A : 1/8B = 3 : 4 ⇒ 8A/5B = 120/160 ⇒ A/B = 120/160 x 5/8 = 15/32 ∴ First part = Rs. (94 x 15/47) = Rs. 30

Question 5

Rs. 680 has been divided among A, B, C such that A gets 2/3 of what B gets 1/4 of what C gets. Then B's share is?

Accepted Answer

Suppose C gets Re.1. Then B gets Re. (1/4) ∴ A gets = Re. (2/3 x 1/4) = Re. 1/6 ∴ A : B : C = 1/6 : 1/4 : 1 = 2 : 3 : 12 Hence B's share = Rs. (680 x 3/17) = Rs. 120

Question 6

Rs. 2430 has been divided among A , B, C in such a way their if their shares be diminished by Rs. 5, Rs.10 and Rs. 15 respectively. The remainders are in the ratio 3 : 4 : 5. Then A's share is?

Accepted Answer

∵ Remainder = Rs. [ 2430 - (5 + 10 + 15)] = Rs. 2400 &there4 A's share = Rs. [ (2400 x 3/12) + 5 ] = Rs. 605

Question 7

The sides of triangle are in the ratio 1/3 : 1/4 : 1/5 and its perimeter is 94 cm. the length of smallest side is?

Accepted Answer

Ratio of sides 1/3 : 1/4 : 1/5 = 20 : 15 : 12 Length of smallest side = 94 x (12/47) cm. = 24 cm.

Question 8

Rs. 53 is divided among A, B and C in such a way that A gets Rs. 7 more than what B gets and B gets Rs. 8 more than what C gets. The ratio of their shares is?

Accepted Answer

Suppose C gets Rs. x Then, B gets Rs. (x + 8) and A gets Rs. (x + 15) ⇒ x + x + 8 + x + 15 = 53 ∴ x =10 so, A : B : C = 25 : 18 : 10

Question 9

A sum of money is divided among A, B, C so that to each rupee A gets, B gets 65 paise and C gets 35 paise. If C's share is Rs. 28, the sum is?

Accepted Answer

A : B : C = 100 : 65 : 35 = 20 : 13 : 7 If C's share is Rs. 7, the sum is Rs. 40. If C's share is Rs. 28, the sum is Rs.(40/7 x 28) = Rs. 160.

Question 10

The incomes of A and B are in the ratio 3 : 2 and their expenditures in the ratio 5 : 3. If each saves Rs. 1,000. A's income is?

Accepted Answer

Let their incomes be 3x, 2x and expenditures 5y, 3y respectively. Then, 3x - 5y = 1000 and 2x - 3y =1000. Solving these equations we get x = 2000, y = 1000 ∴ A's income = 3x = Rs.6000

Question 11

The ratio of the first and second class fares between two stations is 4 : 1 and that of the number of passengers travelling by first and second class is 1 : 40. If Rs. 1100 is collected as fare, the amount collected from first class passengers is?

Accepted Answer

Ratio of amounts collected from 1st and 2nd class = (4 x 1 : 1 x 40) = (1 : 10) ∴Amount collection as 1st class fare = Rs. (1100 x 1/11) = Rs.100

Question 12

The students in three classes are in the ratio 2 : 3 : 5. If 20 students are increased in each class. The ratio changes to 4 : 5 : 7. The total number of students before the increase were?

Accepted Answer

Let the number of students be 2x, 3x and 5x ∴ (2x + 20) : (3x + 20) : (5x + 20) = 4 : 5 : 7 ⇒ (2x + 20)/4 = (3x + 20)/5 = (5x + 20)/7 ⇒ 5(2x + 20) = 4(3x + 20) ∴ x = 10 Hence, total number of student before increase = 10x = 100.

Question 13

One year ago the ratio between Laxman's and Gopal's salary was 3 : 4. The ratio 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. 4,160. The salary…

Accepted Answer

Let the salaries of Laxman and Gopal one year before be x1 ,y1 respectively. ∴ x1/y1 = 3/4 ......(1) x2 + y2 = 4160 .....(2) From equations (1) and (2) x2 = Rs. 1600.

Question 14

Three students A, B and C hired a computer for a month. A runs 27 floppy dics for 19 days, B runs 21 for 17 days and C runs 24 for 23 days. If at the end of the month, the rent amounts to ₹ 23700, how much amount outght to be paid by A?

Accepted Answer

Floppy - days = Number of floppies X Days run Here, A's floppy - days : B 's floppy - days : C's floppy - days = A's payment for rent : B 's payment for rent : C's payment for rent = 27 x 19 : 21 x 17 : 24 x 23 A's rent : B's rent : C's rent = 171 : 119 : 184 ∴ Payment for rent by A = [171/(171 + 119 + 184)] x 23700 = ₹ 8550

Question 15

The work done by (x + 2) men in (x - 3) days and work done by x men in (x - 2) days are equal. Find the value of x.?

Accepted Answer

Work done by (x + 2 ) men in (x - 3) days = (x + 2) (x - 3) Work done by x men in (x - 2) days = x(x - 2) ⇒ (x + 2) (x - 3) = x(x - 2) On Solving, we get x = 6

Question 16

1 yr ago, the ratio between mother and daughter age was 4 : 1. The ratio of their ages after 4 yr will be 3 : 1. Find the ratio of their ages 5 yr ago?

Accepted Answer

Let the present age of mother be x and daughter be y. From question, (x - 1)/(y - 1) = 4/1 ⇒ x - 1 = 4(y - 1) ⇒ x = 4y - 3 ......(i) Again from question, (x + 4)/(y + 4) = 3/1 ∴ x + 4 = 3(y + 4) ⇒ x = 3y + 8 ..(ii) On Solving Eqs. (i) and (ii), we get y = 11 and x = 41 ∴ Ratio of their ages 5 yr ago = (x - 5)/(y - 5) = 36/6 = 6/1 = 6 : 1

Question 17

The ratio of expenditure and saving of a person is 26 : 3 . If his monthly income is ₹ 7250, then what is his monthly savings?

Accepted Answer

Let the expenditure and saving be ₹ 26y and ₹ 3y, respectively. Then, according to the question, 26y + 3y = 7250 ⇒ 29y = 7250 ⇒ y = 7250/29 ⇒ y = 250 So, his monthly saving is (250 x 3) i., e ₹ 750

Question 18

Three hikers A, B and C start on a trip with ₹ 50 each and agree to share the expenses equally. If at the end of the trip, A has ₹ 20 left with him, B ₹ 30 and ₹ 40, by how much amount must they settle their accounts?

Accepted Answer

They start with total of (50 x 3) = ₹ 150 and they return after the trip with (20 + 30 + 40) = ₹ 90. So, to settle their accounts, each person must have 90/3 = ₹ 30 with them, Hence, C must pay ₹ 10 to A

Question 19

₹ 1290 is divided between A, B and C, so that A's share is 1 1/ 2 times B's share and B's share is 1 3/ 4 C's share. What is C's share?

Accepted Answer

A : B = 11/2 = 3 : 2 = 3 x 7 : 2 x 7 = 21 : 14 B : C = 13/4 : 1 = 7 : 4 = 7 x 2 : 4 x 2 = 14 : 8 ∴ A : B : C = 21 : 14 : 8 ∴ C's share = [8/(21 + 14 + 8)] x 1290 = ₹ 240

Question 20

A started a business with a capital of ₹ 10000 and 4 months later , B joined him with a capital of ₹ 5000. What is the share of A in the total profit of ₹ 2000 at the end of the year?

Accepted Answer

Profit of A/Profit of B = (Amount x Number of months) / (Amount x Number of months) = (10000 x 12)/(5000 x 8) = 3/1 ∴ Profit share of A = [3/(3 + 1)] x 2000 = ₹ 1500

Ratio and Proportion Questions