Ratio and Proportions

Ratio & Proportion — Aptitude Questions

Ratio & Proportion — Aptitude Questions

Q1The monthly emoluments of A and B are in the ratio 3 : 4, while the ratio of their expenditures stands at 4 : 5. If A manages to accumulate ₹600 as savings and B retains ₹800, what is A’s monthly income?
Q2Two quantities are in the ratio 5 : 7. If both are augmented by 20 units, the revised proportion becomes 7 : 9. Determine the original numbers.
Solution: Let numbers be 5x and 7x. (5x+20)/(7x+20)=7/9 ⇒ x=10 ⇒ numbers = 50 and 70.
Q3The ratio of the ages of a father and his son is 7 : 3. After 6 years, the ratio transforms into 9 : 5. Ascertain their present ages.
Solution: Let ages be 7x and 3x. (7x+6)/(3x+6)=9/5 ⇒ x=3 ⇒ Father = 21 yrs, Son = 9 yrs.
Q4In a mixture, the proportion of milk to water is 7 : 5. If 15 liters of water is poured in, the ratio alters to 7 : 8. Find the original quantity of milk in the mixture.
Solution: Milk = 7k, Water = 5k. 7k/(5k+15)=7/8 ⇒ k=5 ⇒ Milk = 7×5 = 35 litres.
Q5The stipends of A, B, and C are in the ratio 2 : 3 : 4, while their outlays follow the ratio 3 : 4 : 5. If A saves ₹1600 and B saves ₹2400, determine the savings of C.
Solution: Incomes = 2x,3x,4x; Expenses = 3y,4y,5y. 2x-3y=1600 and 3x-4y=2400 ⇒ y=0, x=800 ⇒ C's saving = 4x-5y = ₹3200.
Q6Two integers are in the ratio 4 : 5. When each is augmented by 20, their ratio becomes 6 : 7. Compute the integers.
Solution: Let 4x and 5x. (4x+20)/(5x+20)=6/7 ⇒ x=10 ⇒ numbers = 40 and 50.
Q7A sum of money is apportioned among A, B, and C in the ratio 3 : 4 : 5. If C receives ₹400 in excess of A, determine the aggregate sum.
Solution: Parts 3k,4k,5k. 5k-3k=2k=400 ⇒ k=200 ⇒ Total = 12k = ₹2400.
Q8Two alloys contain copper and zinc in the ratio 5 : 3 and 1 : 2 respectively. If equal masses of the alloys are fused together, ascertain the resultant proportion of copper to zinc in the new alloy.
Solution: Copper = 5/8 + 1/3 = 23/24; Zinc = 3/8 + 2/3 = 25/24 ⇒ Ratio = 23 : 25.
Q9The ratio of the present ages of A and B is 9 : 5. After 9 years, A’s age will be precisely double that of B’s. Find their present ages.
Note: The plain reading leads to inconsistency (negative solution). If interpreted as "A's age after 9 years equals twice B's present age": 9x+9 = 2(5x) ⇒ x=9 ⇒ A = 81, B = 45.
Q10Three numbers are in the ratio 2 : 3 : 4. If the summation of their cubes is 819, determine the numbers.
Solution: Let numbers 2k,3k,4k. Sum of cubes = 99k^3 = 819 ⇒ k^3 = 91/11 ⇒ k ≈ 2.026 ⇒ Numbers ≈ 4.05, 6.08, 8.10.
Q11It is known that A : B = 2 : 3 and B : C = 4 : 5. What is the compound ratio A : B : C?
Solution: Make B common (LCM 3,4=12) ⇒ A:B = 8:12 and B:C = 12:15 ⇒ A:B:C = 8 : 12 : 15.
Q12A sum of ₹720 is divided among A, B, and C such that A secures two-thirds of B’s share, and B obtains three-fourths of C’s share. What is A’s entitlement?
Solution: A = (2/3)B and B = (3/4)C ⇒ A = (1/2)C. Total = (1/2+3/4+1)C = 9/4 C = 720 ⇒ C=320 ⇒ A = ₹160.
Q13If x : y = 3 : 4 and y : z = 8 : 9, deduce the tripartite ratio x : y : z.
Solution: Align y: take y=8s ⇒ x=6s, z=9s ⇒ x:y:z = 6 : 8 : 9.
Q14The remuneration of A and B are in the ratio 5 : 7. When both salaries are enhanced by ₹600, the ratio modifies to 2 : 3. What is A’s original salary?
Solution: (5x+600)/(7x+600)=2/3 ⇒ leads to x = -600 (no positive solution). The data is inconsistent.
Q15A, B, and C collectively earn ₹3900. If A : B = 2 : 3 and B : C = 4 : 5, determine the individual entitlements of A, B, and C.
Solution: Combine ratios ⇒ A:B:C = 8:12:15 (sum 35). Each part = 3900/35 = 780/7. So A = 8×780/7 = ₹891 3/7, B = ₹1337 1/7, C = ₹1671 3/7.
Puzzle of the dayProblem: You have two jars and 100 red marbles + 100 blue marbles. You need to distribute all marbles into the two jars (you decide how many and which colour go in each) so that the probability of drawing a red marble is maximized. The process: pick a jar at random, then pick a marble randomly from that jar. How do you arrange the marbles?
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