Rs. 750 are divided among A, B and C in such a manner that A : B = 5 : 2 and B : C = 7 : 13, What is B’s share?
Rs. 140
Understanding the Ratio Problem
The problem asks us to divide a total amount of Rs. 750 among three individuals, A, B, and C, based on given ratios between their shares. We are given two separate ratios: A : B and B : C. To find the share of each person from the total amount, we first need to combine these two ratios into a single combined ratio A : B : C.
Combining the Ratios A:B and B:C
We are given:
- A : B = 5 : 2
- B : C = 7 : 13
To combine these ratios, we need to make the value representing B the same in both ratios. The current values for B are 2 and 7. The least common multiple (LCM) of 2 and 7 is 14.
We can rewrite the ratios so that the part corresponding to B is 14:
- For A : B = 5 : 2, multiply both parts by 7: $$A : B = (5 \times 7) : (2 \times 7) = 35 : 14$$
- For B : C = 7 : 13, multiply both parts by 2: $$B : C = (7 \times 2) : (13 \times 2) = 14 : 26$$
Now that the value for B is the same (14) in both ratios, we can combine them to get the combined ratio A : B : C:
$$A : B : C = 35 : 14 : 26$$Calculating the Total Ratio Parts and Value per Part
The combined ratio A : B : C is 35 : 14 : 26.
The total number of ratio parts is the sum of the parts for A, B, and C:
$$Total\ Ratio\ Parts = 35 + 14 + 26$$ $$Total\ Ratio\ Parts = 75$$The total amount to be divided is Rs. 750. The value of one ratio part is calculated by dividing the total amount by the total number of ratio parts:
$$Value\ per\ Part = \frac{Total\ Amount}{Total\ Ratio\ Parts}$$ $$Value\ per\ Part = \frac{750}{75}$$ $$Value\ per\ Part = 10$$So, each ratio part is equal to Rs. 10.
Finding B's Share
From the combined ratio A : B : C = 35 : 14 : 26, the share of B corresponds to 14 parts.
To find B's share in Rupees, we multiply the number of parts for B by the value per part:
$$B's\ Share = Number\ of\ Parts\ for\ B \times Value\ per\ Part$$ $$B's\ Share = 14 \times 10$$ $$B's\ Share = 140$$So, B's share is Rs. 140.
Verifying the Shares
We can also calculate the shares of A and C:
- A's Share = 35 parts \(\times\) Rs. 10/part = Rs. 350
- B's Share = 14 parts \(\times\) Rs. 10/part = Rs. 140
- C's Share = 26 parts \(\times\) Rs. 10/part = Rs. 260
Let's check if the sum of their shares equals the total amount:
$$Total = A's\ Share + B's\ Share + C's\ Share$$ $$Total = 350 + 140 + 260$$ $$Total = 750$$The total is indeed Rs. 750, which matches the given amount. This confirms our calculations are correct.
B's share is Rs. 140.
Important Questions from Compound Ratios
The train fare, bus fare and air fare between 2 places are in the ratio 5 : 8 : 12, the number of passenger travelled by them is in the ratio 3 : 4 : 5 and the total fare collected on a particular day for these modes of transportation for a single trip is Rs. 1,07,000. Find the fare collected from the air passengers.
The compounded ratio of (1 ∶ 3), (6 ∶ 5) and (7 ∶10) is:
Rs. 750 are divided among A, B and C in such a manner that A : B = 5 : 2 and B : C = 7 : 13, What is A’s share?
Two numbers are in the ratio 3 : 5. If 4 is subtracted from each of these two numbers, the new numbers then are in the ratio 4 : 7. Find the smaller of the two original numbers.
A person has some coins of Rs. 10, Rs. 5, and Rs. 2 denominations. The ratio of the products of the numbers of Rs. 10 and Rs. 5 coins, the numbers of Rs. 5 and Rs. 2 coins, and the numbers of Rs. 2 and Rs. 10 coins is 3 ∶ 4 ∶ 2 respectively. What could be the minimum amount of money this person has?
