Learn and practice Problems on ratio and proportion with easy explaination and shortcut tricks. All questions and answers on ratio and proportion covered for various Competitive Exams

Solve Problems:

1) A: B: C is in the ratio of 3: 2: 5. How much money will C get out of Rs 1260?

ATQ, A: B = 1: 2……….. (i) B: C = 3: 2………..(ii) C: D = 1: 3………. (iii) Now, Find A: B: C: D Step 1, A: B: C: D 1: 2 (A: B value by equation i)

Note: To understand the shortcut, remember you need to make the right-hand side missing numbers the same as that of last given number, and for the left-hand side the same is done.

i.e., C: D will contain 2: 2 because 2 is the last number on the right side.

Or, A: B: C: D 1: 2: 2: 2 3: 3: 2: 2 (B: C value by equation ii) 1: 1: 1: 3 (C: D value by equation iii)

Now, multiply vertically and get A: B: C: D.

So, A: B: C: D = (1*3*1): (2*3*1): (2*2*1): (2*2*3) Or, A: B: C: D = 3: 6: 4: 12

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4) 5600 is to be divided into A, B, C, and D in such a way that the ratio of share of A: B is 1: 2, B: C is 3: 1, and C: D is 2: 3. Find the sum of (A and C) and (B and C).

ATQ, A: B = 1: 2……….. (i) B: C = 3: 1……….. (ii) C: D = 2: 3………..(iii) Now, Find A: B: C: D Step 1: A: B: C: D 1: 2 (A: B value by equation i)

Note: To understand the shortcut, remember you need to make the right-hand side missing numbers the same as that of last given number, and for the right-hand side the same is done.

i.e., C: D will contain 2: 2 because 2 is the last number on the right side.

Or, A: B: C: D 1: 2: 2: 2 3: 3: 1: 1 (B: C value by equation ii) 2: 2: 2: 3 (C: D value by equation iii)

Now, multiply vertically and to get A: B: C: D.

So, A: B: C: D = (1*3*2): (2*3*2): (2*1*2): (2*1*3) = 6: 12: 4: 6 = 3: 6: 2: 3

Now, the share of A and C = [(A+C)/ (A+B+C+D)] * total amount Or, the share of A and C = [(3+2)/ (3+6+2+3)] * 5600 Or the share of A and C = (5/14)*5600 = 2000 Similarly, the share of B and C = (8/14)*5600 = 3200

Solution 2:

Find A: B: C: D 1: 2: 2: 2 3: 3: 1: 1 2: 2: 2: 3

Now, multiply vertically and get A: B: C: D.

So, A: B: C: D = (1*3*2): (2*3*2): (2*1*2): (2*1*3) Or, A: B: C: D = 6: 12: 4: 6 Or, A: B: C: D = 3: 6: 2: 3

Sum of the ratios = 3+6+2+3 = 14, but ATQ, it is 5600 Rs. i.e., 14 * 400 = 5600 So, multiply each and every ratio by 400 and get the share of each: 3*400: 6*400: 2*400: 3*400 So, the share of A = 1200 The share of B = 2400 The share of C = 800 The share of D = 1200

Now, the share of (A+C) = 1200+800 = 2000 The share of (B+C) = 2400+ 800 = 3200

5) The ratio of the total amount distributed in all the males and females as salary is 6: 5. The ratio of the salary of each male and female is 2: 3. Find the ratio of the no. of males and females.

The total salary of males: the total salary of females = 6:5 The salary of each male: salary of each female = 2:3

To find the number of men and women, divide the total salary of males and females by salary of each male and female. i.e., 6/2: 5/3 Or, 18: 10 = 9: 5 So, the ratio of the number of males and females = 9:5

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6) The number of employees is reduced in the ratio 3: 2 and the salary of each employee are increased in the ratio 4: 5. By doing so, the company saves Rs. 12000. What was the initial expenditure on the salary?

Initial: Final ATQ, the number of employees: 3 : 2 The salary of each employee: 4 : 5 Then the expenditure will be: 4*3 = 12: 2*5 = 10 12 (initial expenditure): 10 (final expenditure) Or, if the final expenditure = 10, that means the initial expenditure was 12. We can say that the total expenditure reduced by = 12-10 =2units Or, 2 units = 12000 (as it is given that 12000 is saved by the company) So, 1 unit = 6000 Now, the initial expenditure on salary = 12 units *6000 = Rs.72000 [12 comes from ratio 12: 10 where 12 indicates initial expenditure and 10 final expenditure]

7) The ratio of the salary of A and B, one year ago is 3: 2. The ratio of original salary to the increased salary of A is 2: 3 and that of B is 3: 4. The total present salary of A and B together is Rs. 21500. Find the salary of B.

Increased salary of A is 2: 3 that means if it was 2 then it becomes 3. i.e., if it was 2, it becomes 3 Or, 1 becomes 3/2 But the A’s ratio was 3, so we have to calculate for 3 3 becomes (3/2) * 3 = 9/2 = 4.5 Similarly, B?s increase is 3: 4 3 becomes 4 Or, 1 becomes 4/3 But the B’s ratio was 2, so we have to calculate for 2 i.e., 2 become (4/3)* 2 = 8/3

That means if the old ratio of A: B = 3: 2 Then the new ratio of A: B = 4.5: 8/3 So, the new ratio of A: B = 13.5: 8 Now, the salary of B = (B’s share/ Sum of ratios)* total salary Hence, the salary of B = (8/21.5) * 21500 = 8000

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8) The ratio of income of two workers A and B are 3: 4. The ratio of expenditure of A and B is 2: 3 and each saves Rs 200. Find the income of A and B.

Income of A = 3 * 200 = 600 Income of B = 4 * 200 = 800

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9) The ratio of the expenditure of Pervez, Sunny, and Ashu are 16: 12: 9 respectively and their savings are 20%, 25%, 40% of their income. The sum of the income is Rs 1530, find Sunny’s salary.

Let the income of Pervez = x, then the saving = 20x/100 Income of Sunny = y, then the saving = 25y/100 Income of Ashu = z, then the saving = 40z/100

Apply formula

Income – saving = Expenditure

x- 20x/100 = 16 Or, 80x=1600 Or, x = 20

y – 25y/ 100 = 12 Or, 75y/100 = 12 Or, y = 1200/75 = 16

z – 40z/ 100 = 9 Or, 60z/100 = 9 Or, z =15

Now, the ratio of Pervez: Sunny: Ashu = 20: 16: 15 = 51 But ATQ, it is 1530 When 51 is multiplied with 30, we get 1530 So, Sunny’s salary = 16* 30 = 480.

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10) The ratio of income of Pervez, Sunny, and Ashu is 3: 7: 4 and the ratio of their expenditure is 4: 3: 5 respectively. If Pervez saves Rs 300 out of 2400, find the savings of Ashu.

ATQ, income ratio of Pervez: Sunny: Ashu = 3: 7: 4 Let the income of Pervez: Sunny: Ashu = 3x, 7x, 4x The income of Pervez = 3x = 2400 (given in the question) That means x = 2400/3 = 800 Now, the income of Sunny = 7x = 7*800 = 5600 Similarly the income of Ashu = 4x = 4*800 = 3200

Now, Their expenditure is in the ratio of 4: 3: 5 So, let their expenditure is 4y, 3y, 5y The expenditure of Pervez = income of Pervez – saving of Pervez Or, expenditure of Pervez = 4y = 2400-300 = 2100 Or, y = 2100/4 = 525 Here 4y comes from expenditure’s ratio Similarly, the expenditure of Sunny = 3y = 3* 525 = 1575 The expenditure of Ashu = 5y = 5*525 = 2625

Saving’s of Ashu = Income of Ashu – Expenditure of Ashu Saving’s of Ashu = 3200- 2625 = 575