Worked out Problems on Ratio are available for your understanding. Learn how to solve various Ratio Problems by going through the step-by-step solutions provided. Sample Ratio Questions and Answers made available will assist you to learn the concept of ratios easily. Learn the formulas, tips & tricks for solving the ratio problems. All the Ratio Questions and Answers available here are given in a simple and easy-to-understand manner so that you can proceed and enhance your math skills. Become proficient in the concept by having enough practice as it is a must-have skill.

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## Ratio Problems with Solutions PDF

**I. **If X: Y=5: 6, find the value of 3x+2y: 5x+y.

**Solution:**

Given that,

X: Y=5: 6 then X=5k, Y=6k where k is the common multiplier.

Therefore, 3x+2y: 5x+y=3x+2y/5x+y=3(5k)+2(6k)/5(5k)+6k

=15k+12k/25k+6k

=27k/31k

=27:31

Therefore, 3x+2y: 5x+y=27:31.

**II. **Divide 1500 into A, B, C such that A is 3/4th of B and B: C =2:5?

**Solution:**

Given that,

A is 3/4th of B –>A=3/4B–>A/B=3/4

B/C=2/5

For finding A:B: C we have to multiply A/B with 2 and B/C with 4.

A/B=6/8 and B/C=8/20

So A: B: C=6: 8: 20

6x+8x+20x=1500

34x=1500

x=1500/34

=44.11

6x=6(44.11)=264.66

8x=8(44.11)=352.88

20x=20(44.11)=882.2

Therefore, A,B and C will get Rs 264.66,Rs 352.88 and Rs 882.2.

**III. **If (2x + 3y) : (7x – 5y) = 5 : 3 then find the ratio x : y?

**Solution:**

Given that,

(2x + 3y) : (7x – 5y) = 5 : 3

2x+3y/7x-5y=5/3

3(2x+3y)=5(7x-5y)

6x+9y=35x-25y

6x-35x=-25y-9y

-29x=-34y

29x=34y

x/y=34/29

X: Y=34/29

Therefore, X: y=34:29.

**IV. **If a : b = 3 : 8, b : c = 7 : 2 and c : d = 6 : 14 , what is a : d?

**Solution:**

Given that,

a : b = 3 : 8-> a/b=3/8 –>(1)

b: c=7:2-> b/c=7/2 —->(2)

c: d=6:14->c/d=6/14 —>(3)

Multiplying (1),(2), and (3) we get,

a/b × b/c × c/d=3/8 × 7/2 × 6/14

a/d=9/16

Therefore, a:d=9:16.

**V. **If 3A=5B=7C, find A:B: C.

**Solution:**

let 3A=5B=7C=k

3A=k–> A=k/3

5B=k–>B=k/5

7c=k–>C=k/7

A:B:C=?

k/3:K/5:K/7

L.C.M of (3,5,7) is 105.

35k:21k:15k

=35:21:15

Therefore, A:B:C=35:21:15.

**VI. **If x : y=2 : 3,y : z=4 : 7 then find x : z.

## Solution:

Given that,**
**x : y=2 :3,y : z=4 :7

x : y=2 :3 => x/y=2/3

y : z=4 : 7=>y/z=4/7

x/y× y/z=2/3× 4/7

Therefore,x/z=8/21

Hence, x : z=8 : 21

**VII. **A School has 520 students. The ratio of the number of boys to the number of girls is 4:1. This ratio changes to 5:3 after the admission of 80 new students. Find the number of newly admitted girls?

**Solution:**

Given that,

Number of students in the school=520

The ratio of the number of boys to the number of girls is 4:1.

Let the number of boys=4x

Let the number of girls=x

Therefore, 4x+x=520

5x=520

x=520/5=104

Boys=4x=4(104)=416

Girls=x=104

Also given no. of students newly admitted=80

i.e. Total no. of students in the school=520+80=600

The ratio of Boys to Girls=5:3

Let the number of boys be 5x.

Let the number o girls be 3x.

5x+3x=600

8x=600

x=600/8=75

B=5x=5(75)=375

G=3x=3(75)=225

The number of newly admitted Girls=225-104=121

Therefore, the number of newly admitted Girls is 121.

**VIII. **A milkman has a can of 180 liters of milk and water, the ratio of milk and water is 7:2. How much water must be added to the can to make this ratio 4:2?

## Solution:

Given that,

The mixture of milk and water=180 lit

The ratio of milk and water is=7/2

Therefore, Milk/Mix=7/9 (Since mix=milk+water=7+2=9)

Milk=7/9×Mix

Milk=7/9×180=7(20)=140 liters

Water=180-140=40 liters

Let the water added to the mixture be x.

milk/water+x=4/2

140/40+x=4/2

2(140)=4(40+x)

280=160+4x

4x=120

x=120/4=30 liters

Therefore, 30 liters of water should be added to the can.

**IX. **The monthly pocket money of Raju and Sandeep is in the ratio 7:9. Their expenditures are in the ratio 5:7. If each saves Rs 60 every month, find their monthly pocket money?

## Solution:

The monthly pocket money of Raju and Sandeep is in the ratio 7:9.

Let the Raju pocket money be 7x.

Let the Sandeep pocket money b 9x.

Their expenditures are in the ratio 5:7.

Let the Raju expenditure be 5y.

Let the Sandeep expenditure be 7y.

Each saves Rs 60 every month.

i.e. 7x-5y=60–>(1)*7

9x-7y=60 –.(2)*5

49x-35y=480

45x-35y=300

– + –

—————

4x =180

—————-

x=180/4=45

subs x=45 in eq(1)

7(45)-5y=60

315-5y=60

5y=255

y=255/5=51

Monthly pocket money of Raju=7x=7(45)=Rs 315

Monthly pocket money of Sandeep=9x=9(45)=Rs 405

Therefore, The monthly pocket money of Raju and Sandeep are Rs 315 and Rs 405.

**X. **A profit of Rs 8400 is to be shared among three partners in the ratio 3: 4: 5. How much does each partner get?

**Solution:**

Given that,

Profit=Rs 8400

Profit of Rs 8400 has to be shared among three partners in the ratio 3: 4: 5.

Let the first partner share be 3x.

Let the second partner share be 4x.

Let the third partner share be 5x.

3x+4x+5x=8400

12x=8400

x=8400/12=700

So, 3x=3(700)=2100

4x=4(700)=2800

5x=5(700)=3500

Therefore, the shares of the three partners are Rs 2100, Rs 2800, Rs 3500.