If a : b = p : q = 3 : 7, then what is the value of (2a + 3p)/... | Stage I (CBT I) MCQ | Examoogle

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Stage I (CBT I)RRB ALP CBT-I 11 Mar, 2026 Shift 1

If a : b = p : q = 3 : 7, then what is the value of (2a + 3p)/(2b + 3q)?

$\frac{6}{11}$

$\frac{2}{5}$

$\frac{3}{7}$

$\frac{4}{9}$

Correct Answer

📚 GK • GK Direct SubstitutionStage I (CBT I)RRB ALP CBT-I 11 Mar, 2026 Shift 1

Option C

$\frac{3}{7}$

Quick Summary:

Given: Ratio a : b = p : q = 3 : 7.

📐MAMath SolutionDirect Substitution

📋 Given

Ratio a : b = p : q = 3 : 7.

🔢 Formula Used

ab=pq=37  ⟹  a=3k,b=7k,p=3m,q=7m\frac{a}{b} = \frac{p}{q} = \frac{3}{7} \implies a = 3k, b = 7k, p = 3m, q = 7mba​=qp​=73​⟹a=3k,b=7k,p=3m,q=7m

⚡ Exam Hall Shortcut / Speed Trick

Since the ratio of variables in both terms of the expression is identical, you can directly substitute the ratio values: a=3, b=7, p=3, q=7.

⚠️ Common Student Trap / Pitfall

Students often try to find the absolute values of a, b, p, and q, which is impossible as only the ratios are provided.

🔢 Step-by-Step Solution

Substitute ratio values

Since $a/b = p/q = 3/7$ , we can set $a=3, b=7, p=3, q=7$ as a simplified representation.

a=3,b=7,p=3,q=7a=3, b=7, p=3, q=7a=3,b=7,p=3,q=7

Plug values into the expression

Substitute the values into the target expression $(2a + 3p)/(2b + 3q)$ .

2(3)+3(3)2(7)+3(7)\frac{2(3) + 3(3)}{2(7) + 3(7)}2(7)+3(7)2(3)+3(3)​

Perform arithmetic calculation

Calculate the numerator and denominator: Numerator $6 + 9 = 15$ , Denominator $14 + 21 = 35$ .

1535\frac{15}{35}3515​

Simplify the fraction

Divide both numerator and denominator by the common factor $5$ .

15÷535÷5=37\frac{15 \div 5}{35 \div 5} = \frac{3}{7}35÷515÷5​=73​

✅

C is correct because the substitution of the ratio values $a=3, b=7, p=3, q=7$ into the expression yields $15/35$ , which simplifies to $3/7$ .

Core Concepts Used

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💡 EXAM TIP

This property holds for any homogeneous expression of the same degree; if $a/b = c/d$ , then $(ma + nc)/(mb + nd) = a/b$ .

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