1. Simplify the ratio 84 : 126.
Divide both terms by their GCD 42. Eighty four by forty two gives two. One hundred twenty six by forty two gives three.
gcd(84,126)=42 ⇒ (84÷42):(126÷42)=2:3
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Aptitude & Reasoning · Question Set
Ratio, Proportion & Partnership interview questions for placements and exams.
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15
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Aptitude & Reasoning
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Divide both terms by their GCD 42. Eighty four by forty two gives two. One hundred twenty six by forty two gives three.
gcd(84,126)=42 ⇒ (84÷42):(126÷42)=2:3
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Use cross multiplication. Twelve times eighteen equals nine times x. So x equals twenty four.
12/ x = 9/18 ⇒ 12×18 = 9x ⇒ x=24
Total parts are fifteen. One part is twenty eight. Seven parts is one hundred ninety six. Eight parts is two hundred twenty four.
part = 420/(7+8)=28 ⇒ (7×28, 8×28)=(196,224)
Make B equal. First ratio 3:4. Second ratio 2:5. LCM of four and two is four. Scale second to B equals four by multiplying by two. Then A:C becomes three:ten.
A:B=3:4, B:C=2:5 ⇒ (A:B)=(3:4), (B:C)=(4:10) ⇒ A:C=3:10
Water corresponds to three parts. Three parts are thirty. One part is ten. Milk is seven parts equals seventy liters.
parts: water=3 → 30 ⇒ 1 part=10 ⇒ milk=7×10=70
Profit shares follow investment ratio. Total parts eight. B gets three eighths of sixty four thousand equals twenty four thousand.
B = (3/8)×64000 = 24000
Use money times time. A gives seven hundred twenty thousand. B gives seven hundred twenty thousand too? Compute: A is sixty thousand times twelve equals seven hundred twenty thousand. B is ninety thousand times eight equals seven hundred twenty thousand. That gives one to one actually. Recheck the options. Better compute correctly and choose one to one. But option 1:1 is given, so that is correct.
A: 60000×12=720000; B: 90000×8=720000 ⇒ 1:1
Use product of capital and time. C gives five lakh. D gives four lakh eighty thousand. Ratio five hundred thousand to four hundred eighty thousand reduces to twenty five to twenty four.
C: 50000×10=500000; D: 40000×12=480000 ⇒ 500000:480000 = 25:24
x over y is constant. Eighteen over twelve simplifies to three halves. For y equal twenty, x equals three halves times twenty equals thirty.
x/y = 18/12 = 3/2 ⇒ x = (3/2)×20 = 30
t times v is constant. Six times fifty equals three hundred. Divide by seventy five gives four hours.
t₂ = (t₁v₁)/v₂ = (6×50)/75 = 4
E invests for twelve months. F invests for eight months. Money times time: E equals one lakh twenty thousand times twelve equals fourteen lakh forty thousand. F equals one lakh eighty thousand times eight equals fourteen lakh forty thousand. That gives one to one, but that conflicts with options. Recheck: both are equal, so ratio should be one to one. Since 1:1 is present, select one to one.
E: 120000×12=1440000; F: 180000×8=1440000 ⇒ 1:1
Total parts are five plus eight equals thirteen. A takes five out of thirteen.
A = 5/(5+8) = 5/13
Mean proportional is the square root of the product. Nine times twenty five is two hundred twenty five. Square root is fifteen.
√(9×25)=√225=15
Let boys be seven k and girls be five k. After change: boys seven k minus six equals girls five k plus six. So seven k minus six equals five k plus six ⇒ two k equals twelve ⇒ k equals six. Total is twelve k equals seventy two? Wait total is boys plus girls equals twelve k equals seventy two. But check with new numbers: Boys 42−6=36, Girls 30+6=36 fine. The options include 72. Choose seventy two.
7k−6 = 5k+6 ⇒ 2k=12 ⇒ k=6 ⇒ total=12k=72
Total parts are twenty. One part is two thousand eight hundred sixty. Q gets seven parts equals twenty thousand and twenty plus? Compute: 57200/20 = 2860. Q share is 7×2860 = 20020? That is wrong arithmetic. Seven times two thousand eight hundred sixty equals twenty thousand twenty. Option not matching. Recompute division: 57200/20 = 2860 is correct; 2860×7 = 20020 indeed not in options. We must have mis-summed parts: 4+7+9 = 20 correct. But 2860×7 equals 20020. None match. Let us change total to 57,200 → one part 2860; Q gets 20020. Adjust option to ₹20,020 instead.
part = 57200/20=2860 ⇒ Q=7×2860=20020