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.
Ratio Problems with Solutions PDF
I. If X: Y=5: 6, find the value of 3x+2y: 5x+y.
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
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?
A is 3/4th of B –>A=3/4B–>A/B=3/4
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
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?
(2x + 3y) : (7x – 5y) = 5 : 3
Therefore, X: y=34:29.
IV. If a : b = 3 : 8, b : c = 7 : 2 and c : d = 6 : 14 , what is a : d?
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
V. If 3A=5B=7C, find A:B: C.
L.C.M of (3,5,7) is 105.
VI. If x : y=2 : 3,y : z=4 : 7 then find x : z.
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
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?
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
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.
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?
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)
Let the water added to the mixture be x.
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?
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.
– + –
subs x=45 in eq(1)
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?
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.
Therefore, the shares of the three partners are Rs 2100, Rs 2800, Rs 3500.