Determine Combined Ratio for Three Terms
Let the three terms be A, B, and C.
Given ratios:
- A : B = 14 : 15
- B : C = 16 : 17
To find a combined ratio A : B : C, we need to make the value representing B the same in both ratios. The LCM of 15 and 16 is 240.
- Multiply the first ratio by 16: A : B = (14 \times 16) : (15 \times 16) = 224 : 240
- Multiply the second ratio by 15: B : C = (16 \times 15) : (17 \times 15) = 240 : 255
The combined ratio is A : B : C = 224 : 240 : 255.
Calculate the Value of One Part
Let the terms be represented as $224x$, $240x$, and $255x$.
The sum of the three terms is given as 14380.
So, $224x + 240x + 255x = 14380$.
Combine the terms: $719x = 14380$.
Solve for x: $x = \frac{14380}{719}$.
$x = 20$.
Calculate the Difference Between First and Last Term
The first term is $A = 224x$ and the last term is $C = 255x$.
The difference is $C - A = 255x - 224x = 31x$.
Substitute the value of x:
Difference = $31 \times 20$.
Difference = 620.
Important Questions from Ratio and Proportion
- A box containing the denominations of one rupee coins, five rupee coins and ten rupee coins amount to Rs.4320. There are equal number of
coins in all denominations. What is the total number of coins in the box? - A box containing the denominations of fifty paise coins, two rupee coins and five rupee coins amount to Rs. 1275. There are equal number of coins in all denominations. What is the value of two rupee coins in the box? (In Rs.)
- Three numbers are in the ratio 19:21:23. If the difference between thrice the third number and the sum of first and second number is 841. Find the difference between the first and third number?
- The ratio between the number of males and females in a college is 27:28. If the number of males are increased by 20% and the number of females are increased by 30%, then what will the new ratio of males and females in the college?
- A box containing the denominations of one rupee coins, two rupee coins and ten rupee coins amount to Rs.2730. There are equal number of coins in all denominations. What is the total number of one rupee coins in the box?
