Question:
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 ______?
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 ______?
Show Hint
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
- 88
- 96
- 102
- 112
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Assign variables to each part of the score.
Let the byes be \(x\) runs, the wides be \(y\) runs, and the combined runs scored by Ram and Shyam be \(z\) runs. Since the team lost no wicket, these three parts add up to the full total: \(x + y + z = 232\).
Step 2: Turn the two clues into equations.
"The runs scored by the two batsmen are 26 times the wides" means \(z = 26y\).
"There are 8 more byes than wides" means \(x = y + 8\).
Step 3: Substitute both into the total-runs equation.
\[ (y + 8) + y + 26y = 232 \]
\[ 28y + 8 = 232 \]
\[ 28y = 224 \]
\[ y = 8 \]
So wides \(= 8\), byes \(x = 8 + 8 = 16\), and batsmen runs \(z = 26 \times 8 = 208\). As a check, \(16 + 8 + 208 = 232\), which matches the given total.
Step 4: Split the batsmen's 208 runs in the ratio \(6 : 7\).
Let Ram's runs be \(6r\) and Shyam's runs be \(7r\), so \(6r + 7r = 208\), which gives \(13r = 208\) and \(r = 16\).
Ram's runs \(= 6 \times 16 = 96\). Shyam's runs \(= 7 \times 16 = 112\).
Final Answer:
Ram scored 96 runs. Note that 112 is actually Shyam's score, not Ram's, and is a common mix-up; 88 and 102 do not divide evenly by 6 to give a whole \(r\) that fits the total of 208, so neither can be correct.
\[ \boxed{96} \]
Let the byes be \(x\) runs, the wides be \(y\) runs, and the combined runs scored by Ram and Shyam be \(z\) runs. Since the team lost no wicket, these three parts add up to the full total: \(x + y + z = 232\).
Step 2: Turn the two clues into equations.
"The runs scored by the two batsmen are 26 times the wides" means \(z = 26y\).
"There are 8 more byes than wides" means \(x = y + 8\).
Step 3: Substitute both into the total-runs equation.
\[ (y + 8) + y + 26y = 232 \]
\[ 28y + 8 = 232 \]
\[ 28y = 224 \]
\[ y = 8 \]
So wides \(= 8\), byes \(x = 8 + 8 = 16\), and batsmen runs \(z = 26 \times 8 = 208\). As a check, \(16 + 8 + 208 = 232\), which matches the given total.
Step 4: Split the batsmen's 208 runs in the ratio \(6 : 7\).
Let Ram's runs be \(6r\) and Shyam's runs be \(7r\), so \(6r + 7r = 208\), which gives \(13r = 208\) and \(r = 16\).
Ram's runs \(= 6 \times 16 = 96\). Shyam's runs \(= 7 \times 16 = 112\).
Final Answer:
Ram scored 96 runs. Note that 112 is actually Shyam's score, not Ram's, and is a common mix-up; 88 and 102 do not divide evenly by 6 to give a whole \(r\) that fits the total of 208, so neither can be correct.
\[ \boxed{96} \]
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