Question

The ratio of two numbers is 3:4. If their sum is 70, what is the larger number?

• A. 30
• B. 40
• C. 50
• D. 60

Hint:

Express numbers as multiples of the ratio and solve for the variable using the sum.

Answer 1

The Correct Option is B

We need to find the larger number.
- Step 1: Define numbers. Let the numbers be \( 3x \) and \( 4x \), since ratio is 3:4.
- Step 2: Set up sum equation.
\[ 3x + 4x = 70 \Rightarrow 7x = 70 \] - Step 3: Solve for \( x \).
\[ x = \frac{70}{7} = 10 \] - Step 4: Find numbers.
- Smaller: \( 3x = 3 \times 10 = 30 \).
- Larger: \( 4x = 4 \times 10 = 40 \).
- Step 5: Verify. Sum: \( 30 + 40 = 70 \). Ratio: \( 30 : 40 = 3 : 4 \). Correct.
- Step 6: Check options.
- (a) 30: Smaller number.
- (b) 40: Correct, larger number.
- (c) 50: Incorrect.
- (d) 60: Incorrect.
- Step 7: Alternative approach. Solve using equations: Let numbers be \( a \) and \( b \). \( \frac{a}{b} = \frac{3}{4} \), \( a + b = 70 \). Then \( a = \frac{3}{4}b \). Substitute:
\[ \frac{3}{4}b + b = 70 \Rightarrow \frac{7}{4}b = 70 \Rightarrow b = 40 \Rightarrow a = 30 \] Larger = 40.
Thus, the answer is b.