Ratio Calculation for Chandan's Share
The question asks to find the number of pencils Chandan received when 330 pencils are distributed among Rajesh, Suresh, and Chandan in a specific ratio.
Step 1: Simplify the Ratio
The given ratio is $\frac{1}{4} : \frac{2}{3} : \frac{1}{3}$. To simplify this fractional ratio into whole numbers, we find the Least Common Multiple (LCM) of the denominators (4, 3, and 3). The LCM is 12.
Multiply each part of the ratio by the LCM (12):
- Rajesh's share ratio: $\frac{1}{4} \times 12 = 3$
- Suresh's share ratio: $\frac{2}{3} \times 12 = 8$
- Chandan's share ratio: $\frac{1}{3} \times 12 = 4$
The simplified ratio is $3 : 8 : 4$.
Step 2: Calculate the Sum of Ratio Parts
Add the parts of the simplified ratio to find the total number of parts:
Sum of parts = $3 + 8 + 4 = 15$
Step 3: Calculate Chandan's Share
Chandan's share corresponds to 4 parts out of the total 15 parts. The total number of pencils is 330.
Chandan's pencils = $\left(\frac{\text{Chandan's ratio part}}{\text{Sum of ratio parts}}\right) \times \text{Total pencils}$
Chandan's pencils = $\frac{4}{15} \times 330$
Calculation:
Chandan's pencils = $4 \times \frac{330}{15}$
Chandan's pencils = $4 \times 22$
Chandan's pencils = $88$
Therefore, Chandan received 88 pencils.
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Important Questions from Ratio and Proportion
In a mixture of 156 litres, the ratio of milk and water is 7 : 6. How much water should be added to make the ratio 14 : 13?
If the ratio of the first to second number is 3 : 4 and that of the second to the third number is 8 : 5, and sum of three numbers is 190 then the third number is:
The third proportional to 9 and 15 is:
The average age of 3 persons is 30 years.If their ages are in the ratio of 3 : 5 : 7 respectively, then the age of the eldest person is:
The income of A and B are in the ratio 5 : 3. The expenses of A, B and C are in the ratio of 8 : 5 : 2. If C spends 2000 and B saves ₹ 700, then A saves:
