Question:medium

In a cricket match, Team A scored 232 runs without losing a wicket. The score was made up of byes, wides and runs scored by the two opening batsmen, Ram and Shyam. The runs scored by the two batsmen are 26 times the wides. There are 8 more byes than wides. If the ratio of the runs scored by Ram and Shyam is \(6:7\), then the runs scored by Ram is ______?

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Write byes and the batsmen's combined runs in terms of the wides, then use the total of 232 to pin down the wides first.
Updated On: Jul 10, 2026
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The Correct Option is B

Solution and Explanation

Step 1: Work with the batsmen's total runs, $z$, as the only unknown.
Since the runs scored by the two batsmen are 26 times the wides, if wides $= y$ then $z = 26y$, so $y = \dfrac{z}{26}$.

Step 2: Write byes in terms of $z$ too.
Byes are 8 more than wides, so byes $= y + 8 = \dfrac{z}{26} + 8$.

Step 3: Use the total score to solve for $z$ directly.
The full score is byes $+$ wides $+$ batsmen runs $= 232$:
\[ \left(\frac{z}{26} + 8\right) + \frac{z}{26} + z = 232 \]
\[ \frac{2z}{26} + z + 8 = 232 \]
\[ \frac{z}{13} + z = 224 \]
Multiply every term by 13 to clear the fraction:
\[ z + 13z = 224 \times 13 \]
\[ 14z = 2912 \]
\[ z = 208 \]
This confirms the batsmen scored 208 runs between them, without solving for wides or byes first.

Step 4: Divide 208 in the ratio $6 : 7$.
The total number of ratio parts is $6 + 7 = 13$, so one part is worth $\dfrac{208}{13} = 16$ runs. Ram's share is the "6" part, so Ram scored $6 \times 16 = 96$ runs.

Final Answer:
$z = 208$, split $6:7$ gives Ram $= 96$ runs.
\[ \boxed{96} \]
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