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.