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Aptitude & Reasoning · Question Set
Averages, Mixtures & Allegations interview questions for placements and exams.
Questions
12
Included in this set
Subject
Aptitude & Reasoning
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Difficulty
Mixed
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Go through each question and its explanation. Use this set as a focused practice pack for Aptitude & Reasoning.
Total needed is five times twenty six equals one hundred thirty. Known sum is one hundred four. The missing number is twenty six.
x = 5×26 − (18+24+30+32) = 130 − 104 = 26
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Total parts are four. One part equals ten liters. Water is one part, so ten liters.
water = 40 × (1/(3+1)) = 10
Average times count equals sum. Fifteen times eight equals one hundred twenty. This is the total of the numbers.
sum = avg × n = 15 × 8 = 120
Original sum is twelve times twenty equals two hundred forty. Add thirty two to get two hundred seventy two. Divide by thirteen to get twenty one.
newAvg = (12×20 + 32)/13 = 272/13 = 21
Total is ten times eighteen equals one hundred eighty. Remove twenty eight to get one hundred fifty two. Divide by nine to get seventeen.
newAvg = (10×18 − 28)/9 = 152/9 ≈ 17
Use weighted average. Total sum equals twenty times seventy plus thirty times eighty equals one thousand four hundred plus two thousand four hundred equals three thousand eight hundred. Divide by total fifty to get seventy six.
avg = (20×70 + 30×80)/(20+30) = 3800/50 = 76
Error adds thirty six to the total. Correct sum is old sum plus thirty six. Old sum is 40×56 = 2240. New sum is 2276. Divide by forty to get fifty six point nine.
newMean = (40×56 + 36)/40 = 2276/40 = 56.9
Apply allegation. High minus mean equals three hundred minus two sixty equals forty. Mean minus low equals two sixty minus two hundred equals sixty. Ratio low to high equals forty to sixty equals two to three.
ratio = (300−260):(260−200)=40:60=2:3
Set up acid balance. Let x be liters of thirty percent. Acid: 0.3x + 0.5×20 equals 0.4(x+20). Solve: 0.3x + 10 = 0.4x + 8 ⇒ x = 20.
0.3x+10 = 0.4(x+20) ⇒ x=20
Alcohol amount stays at six liters. Let final volume be V. Six equals zero point one five V, so V equals forty. Added water is forty minus thirty equals ten liters.
0.20×30 = 0.15×V ⇒ V=40 ⇒ add=10
Use dilution factor. Each time, fraction kept is 1 − 12/60 = 0.8. After two steps, salt amount is initial salt times 0.8 squared. Initial salt is 0.25×60 = 15 L. Final salt is 15×0.64 = 9.6 L. Concentration is 9.6 / 60 = 0.16? Wait volume stays 60, yes. But replacement with water keeps total 60 each time. After two steps salt is 9.6 L, so 9.6/60 = 0.16 or 16%. Correct answer is 16%.
salt = 15×(1−12/60)^2 = 15×0.64 = 9.6 ⇒ % = 9.6/60=16%
Use the replacement formula. After each operation milk remains in the same fraction. Remaining fraction after one step is fifteen over twenty equals three fourths. After two steps milk equals twenty times three fourths squared equals eleven point two five liters.
milk = 20×(1 − 5/20)^2 = 20×(3/4)^2 = 11.25