MCQ
Ratio and Proportion MCQ - Practice Questions with Answers
Solve 12 Ratio and Proportion questions for RAS/RPSC preparation.
Practice questions
Q1A 180-litre blend of three liquids is mixed in the ratio 2 : 3 : 4. Then 36 litres of the blend are drawn off and replaced with an equal volume of the third liquid alone. What is the new ratio of the three liquids?
Originally the liquids are 40 L, 60 L and 80 L. Drawing 36 L removes 8 L, 12 L and 16 L in the same 2 : 3 : 4 split, leaving 32 L, 48 L and 64 L. Replacing with 36 L of the third liquid raises it to 100 L, so the new ratio is 32 : 48 : 100 = 8 : 12 : 25.
Q2The profit of ₹9450 is shared by three partners in the ratio 2 : 3 : 4. If the middle partner then transfers ₹450 of his share to the first partner, what is the new difference between the third partner's amount and the first partner's amount?
The nine equal parts of ₹9450 give a unit of ₹1050, so the original shares are ₹2100, ₹3150 and ₹4200. After ₹450 moves from the middle partner to the first, the amounts become ₹2550, ₹2700 and ₹4200. The new difference between the third and the first is 4200 − 2550 = ₹1650.
Q3Three storage tanks hold diesel in the ratio 3 : 4 : 7. After 21 litres are pumped from the largest tank into the smallest, the smallest and the middle tanks contain equal volumes. How many litres were originally in the largest tank?
Let the original volumes be 3k, 4k and 7k litres. After moving 21 litres, the smallest becomes 3k + 21 and equals the middle tank 4k, so 3k + 21 = 4k and k = 21. The largest tank originally held 7 × 21 = 147 litres.
Q4Three heirs inherit an estate in the ratio 2 : 3 : 5. The first heir gifts one-fourth of her inheritance to the second; the second then gifts one-fifth of his updated amount to the third. If the third heir finally holds ₹2280, what was the size of the estate?
Let the original shares be 2k, 3k and 5k. After the first gift, the amounts are 3k/2 and 7k/2 for the first two heirs. The second then gives one-fifth of 7k/2, namely 7k/10, to the third, so the third finally has 5k + 7k/10 = 57k/10. Setting 57k/10 = 2280 gives k = 400, and the estate totals 10k = ₹4000.
Q5The sides of a triangular plot are in the ratio 5 : 7 : 8 and the perimeter is 100 m. If each side is lengthened by 5 m, by what percentage does the perimeter increase?
Twenty equal parts make up the 100 m perimeter, so the sides are 25 m, 35 m and 40 m. Lengthening each side by 5 m adds 15 m in total. The percentage increase is (15 / 100) × 100% = 15%.
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More questions
6Daily carton counts from three packing machines stand in the ratio 5 : 4 : 3. After an upgrade the first machine's count rises by 25%, while the third machine packs 12 fewer cartons than before, and the new counts are in the ratio 25 : 16 : 9. What was the second machine's original daily count?
7If three measured lengths are in the ratio 1 : 3 : 5 and their total is 135 cm, what is the sum of the shortest and the longest lengths?
8Given A : B = 5 : 6 and B : C = 4 : 7, express A : B : C.
9Three partners divide a year's profit in the ratio 5 : 7 : 8. If the second partner receives ₹2,100 more than the first, what percentage of the total profit goes to the third partner?
10A warehouse stores cement and sand in the ratio 9 : 4. After 30 kg of cement is used up and 10 kg of sand is added, the ratio becomes 3 : 2. How many kilograms of sand were originally stored?
11The filling rates of three pumps are in the ratio 4 : 5 : 6. If the first pump is sped up by 50% and the third is slowed to two-thirds of its present rate, what is the new ratio of their filling rates?
12Three co-workers' wages are in the ratio 1/2 : 1/3 : 1/4. After the first wage is cut by ₹90 and the second is raised by ₹60, those two wages become equal. What was the third co-worker's original wage?