Ratio and Proportion worksheet for Class 6 students, featuring math problems and a multiple-choice question about cricket runs.

Here are the step-by-step solutions for each question on the worksheet.

(1) Ratio of Rail:Roads, Roads:Rivers, and Rail:Rivers
* Given: Rail = 3910 km, Roads = 9860 km, Rivers = 16490 km.
* Step 1 (Rail : Roads):
$3910 : 9860$. Divide both by 10 $\rightarrow$ $391 : 986$.
Both numbers are divisible by 17 ($391 \div 17 = 23$ and $986 \div 17 = 58$).
Result: 23:58
* Step 2 (Roads : Rivers):
$9860 : 16490$. Divide both by 10 $\rightarrow$ $986 : 1649$.
Both numbers are divisible by 17 ($986 \div 17 = 58$ and $1649 \div 17 = 97$).
Result: 58:97
* Step 3 (Rail : Rivers):
$3910 : 16490$. Divide both by 10 $\rightarrow$ $391 : 1649$.
Both numbers are divisible by 17 ($391 \div 17 = 23$ and $1649 \div 17 = 97$).
Result: 23:97

(2) Ratio of working time to break time
* Total Time: From 07:30 AM to 06:15 PM is 10 hours and 45 minutes.
Convert to minutes: $(10 \times 60) + 45 = 645$ minutes.
* Break Time:
Lunch: 45 mins.
Coffee: $2 \times 15 = 30$ mins.
Total Breaks: $45 + 30 = 75$ minutes.
* Working Time: Total Time - Break Time = $645 - 75 = 570$ minutes.
* Ratio (Work : Breaks):
$570 : 75$. Divide both by 15.
$570 \div 15 = 38$.
$75 \div 15 = 5$.
Result: 38:5

(3) Number used to simplify a ratio
To write a ratio in its simplest form, you must divide both terms by their Highest Common Factor (HCF) (also known as the Greatest Common Divisor).

(4) Right answers vs Wrong answers
* Ratio: Right : Wrong = 11 : 10.
* Given: Wrong answers = 40.
* Since the "Wrong" part of the ratio is 10, and the actual number is 40, we multiplied by 4 ($10 \times 4 = 40$).
* Do the same for the "Right" part: $11 \times 4 = 44$.
Result: 44 right answers

(5) Ratio of Sneha's salary to Alisha's salary
* Sneha: 36800.
* Alisha: Rs. 24000 *more* than Sneha. So, $36800 + 24000 = 60800$.
* Ratio (Sneha : Alisha):
$36800 : 60800$. Cancel zeros $\rightarrow$ $368 : 608$.
Divide by 16 $\rightarrow$ $23 : 38$.
Result: 23:38

(6) Ratio of boys to girls
* Total students: 1150.
* Girls: 600.
* Boys: $1150 - 600 = 550$.
* Ratio (Boys : Girls):
$550 : 600$. Cancel zeros $\rightarrow$ $55 : 60$.
Divide by 5 $\rightarrow$ $11 : 12$.
Result: 11:12

(7) Name of the second term
In a ratio $a:b$, the first term ($a$) is the antecedent, and the second term ($b$) is called the consequent.

(8) Ratio of width to perimeter
* Width: 25 cm.
* Length: 45 cm.
* Perimeter: $2 \times (\text{Length} + \text{Width}) = 2 \times (45 + 25) = 2 \times 70 = 140$ cm.
* Ratio (Width : Perimeter):
$25 : 140$. Divide both by 5.
$25 \div 5 = 5$.
$140 \div 5 = 28$.
Result: 5:28

(9) Ratio of speeds
Since they travel for the same time (6 hours), the ratio of their speeds is the same as the ratio of the distances they traveled.
* Rajesh: 180 km.
* Sarika: 222 km.
* Ratio: $180 : 222$. Divide both by 6.
$180 \div 6 = 30$.
$222 \div 6 = 37$.
Result: 30:37

(10) Multiple Choice Question
* First Team Score: 79 runs.
* Second Team Score: 35 runs.
* Runs Needed to Win: To win, the second team needs 1 more run than the first team.
$79 + 1 = 80$ runs needed.
* Ratio (Made : Need):
$35 : 80$. Divide both by 5.
$35 \div 5 = 7$.
$80 \div 5 = 16$.
Result: 7:16 (Option b)

Final Answer:
(1) Rail:Roads = 23:58, Roads:Rivers = 58:97, Rail:Rivers = 23:97
(2) 38:5
(3) Highest Common Factor (HCF)
(4) 44
(5) 23:38
(6) 11:12
(7) Consequent
(8) 5:28
(9) 30:37
(10) b. 7:16