Home›MPPSC Prelims›Paper 2: General Aptitude Test (CSAT)›General Aptitude›Logical Reasoning and Analytical Ability›Deductive & Inductive Reasoning, Syllogisms, Series, Coding-Decoding›If x stand for -, ÷ stands for +, + stands for ÷ and - stands for x,

If x stand for -, ÷ stands for +, + stands for ÷ and - stands for x, then arrange the following in increasing order :
1. 15 - 5 ÷ 5 x 20 + 10
2. 8 ÷ 10 - 3 + 5 x 6
3. 6 x 2 + 3 ÷ 12 - 3
4. 3 ÷ 7 - 5 x 10 + 3
Choose the correct answer from the code given below :

20242Mprelimsyear-2024p2
A.(A) 4, 1, 3, 2
B.(B) 2, 4, 3, 1Correct
C.(C) 4, 3, 2, 1
D.(D) 2, 4, 1, 3
Explanation & Solution

The correct answer is (B) 2, 4, 3, 1.

Step-by-step operator replacement & evaluation:

  • Operator replacement rules: ×→−,  ÷→+,  +→÷,  −→××\times× \to -, \; ÷\div÷ \to +, \; + \to ÷\div÷, \; - \to ×\times××→−,÷→+,+→÷,−→×.
  • Expression 1: 15×5+5−20÷10=(15×5)+5−(20÷10)=75+5−2=7815 ×\times× 5 + 5 - 20 ÷\div÷ 10 = (15 ×\times× 5) + 5 - (20 ÷\div÷ 10) = 75 + 5 - 2 = 7815×5+5−20÷10=(15×5)+5−(20÷10)=75+5−2=78.
  • Expression 2: 8+10×3÷5−6=8+(10×3÷5)−6=8+6−6=88 + 10 ×\times× 3 ÷\div÷ 5 - 6 = 8 + (10 ×\times× 3 ÷\div÷ 5) - 6 = 8 + 6 - 6 = 88+10×3÷5−6=8+(10×3÷5)−6=8+6−6=8.
  • Expression 3: 6−2÷3+12×3=6−(2÷3)+(12×3)=6−0.67+36=41.336 - 2 ÷\div÷ 3 + 12 ×\times× 3 = 6 - (2 ÷\div÷ 3) + (12 ×\times× 3) = 6 - 0.67 + 36 = 41.336−2÷3+12×3=6−(2÷3)+(12×3)=6−0.67+36=41.33.
  • Expression 4: 3+7×5−10÷3=3+(7×5)−(10÷3)=3+35−3.33=34.673 + 7 ×\times× 5 - 10 ÷\div÷ 3 = 3 + (7 ×\times× 5) - (10 ÷\div÷ 3) = 3 + 35 - 3.33 = 34.673+7×5−10÷3=3+(7×5)−(10÷3)=3+35−3.33=34.67.
  • Arranging in increasing numerical order: Expression 2 (8)<Expression 4 (34.67)<Expression 3 (41.33)<Expression 1 (78)  ⟹  <strong>2,4,3,1</strong>Expression 2 \text{Expression 2 }Expression 2  (8) < Expression 4 \text{Expression 4 }Expression 4  (34.67) < Expression 3 \text{Expression 3 }Expression 3  (41.33) < Expression 1 \text{Expression 1 }Expression 1  (78)   ⟹  \implies⟹ <strong>2, 4, 3, 1</strong>Expression 2 (8)<Expression 4 (34.67)<Expression 3 (41.33)<Expression 1 (78)⟹<strong>2,4,3,1</strong>.

हिंदी में प्रश्न एवं आदर्श उत्तर

यदि x का अर्थ - है, ÷ का अर्थ + है, + का अर्थ ÷ है और - का अर्थ x है, तो निम्नलिखित को बढ़ते हुए क्रम में व्यवस्थित कीजिए :
1. 15 - 5 ÷ 5 x 20 + 10
2. 8 ÷ 10 - 3 + 5 x 6
3. 6 x 2 + 3 ÷ 12 - 3
4. 3 ÷ 7 - 5 x 10 + 3
नीचे दिए गए कूट से सही उत्तर चुनिए :

A.(A) 4, 1, 3, 2
B.(B) 2, 4, 3, 1सही
C.(C) 4, 3, 2, 1
D.(D) 2, 4, 1, 3

सही उत्तर (B) 2, 4, 3, 1 है।

गणितीय संक्रियाओं का चरणबद्ध मान:

  • चिन्ह परिवर्तन: ×→−,  ÷→+,  +→÷,  −→××\times× \to -, \; ÷\div÷ \to +, \; + \to ÷\div÷, \; - \to ×\times××→−,÷→+,+→÷,−→×।
  • समीकरण 1: 15×5+5−20÷10=75+5−2=7815 ×\times× 5 + 5 - 20 ÷\div÷ 10 = 75 + 5 - 2 = 7815×5+5−20÷10=75+5−2=78।
  • समीकरण 2: 8+10×3÷5−6=8+6−6=88 + 10 ×\times× 3 ÷\div÷ 5 - 6 = 8 + 6 - 6 = 88+10×3÷5−6=8+6−6=8।
  • समीकरण 3: 6−2÷3+12×3=6−0.67+36=41.336 - 2 ÷\div÷ 3 + 12 ×\times× 3 = 6 - 0.67 + 36 = 41.336−2÷3+12×3=6−0.67+36=41.33।
  • समीकरण 4: 3+7×5−10÷3=3+35−3.33=34.673 + 7 ×\times× 5 - 10 ÷\div÷ 3 = 3 + 35 - 3.33 = 34.673+7×5−10÷3=3+35−3.33=34.67।
  • बढ़ते क्रम (आरोही क्रम) में व्यवस्थित करने पर: 2(8)<4(34.67)<3(41.33)<1(78)  ⟹  <strong>2,4,3,1</strong>2 (8) < 4 (34.67) < 3 (41.33) < 1 (78)   ⟹  \implies⟹ <strong>2, 4, 3, 1</strong>2(8)<4(34.67)<3(41.33)<1(78)⟹<strong>2,4,3,1</strong>।
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