Advertisements
Advertisements
Question
If a : b = 9 : 10, find the value of `(2a^2 - 3b^2)/(2a^2 + 3b^2)`
Advertisements
Solution
a : b = 9 : 10
⇒ `a/b = (9)/(10)`
`(2a^2 - 3b^2)/(2a^2 + 3b^2)`
= `((2a^2)/(b^2) - (3b^2)/(b^2))/((2a^2)/(b^2) - (3b^2)/(b^2))` ...(Dividing by b2)
= `(2(a/b)^2 - 3)/(2(a/b)^2 + 3`
= `(2(9/10)^2 - 3)/(2(9/10)^2 + 3)`
= `(2 xx 81/100 - 3)/(2 xx 81/100 + 3)`
= `(81/50 - 3)/(81/50 + 3)`
= `((81 - 150)/(50))/((81 + 150)/(50)`
= `(-69)/(50) xx (50)/(231)`
= `(-69)/(231)`
= `-(23)/(77)`
RELATED QUESTIONS
In a basket, the ratio between the number of oranges and the number of apples is 7 : 13. If 8 oranges and 11 apples are eaten, the ratio between the number of oranges and the number of apples becomes 1 : 2. Find the original number of oranges and the original number of apples in the basket.
`square` ABCD is a parallelogram. The ratio of `angle`A and `angle`B of this parallelogram is 5 : 4. Find the measure of `angle`B.
Find the reciprocal ratio of e following :
a3b2 : a2b3
Express the following ratios in its simplest form :
`1 1/2:2 1/2`
Is the ratio of 6 g and 15 g same as the ratio of 36 cm and 90 cm ?
If A : B = 2 : 3, B : C = 4 : 5 and C : D = 6 : 7, find A : D
Express the following ratio in the simplest form:
85 : 561
Find the ratio of:
150 mL to 2 L
If a bus travels 160 km in 4 hours and a train travels 320 km in 5 hours at uniform speeds, then the ratio of the distances travelled by them in one hour is ______.
225% is equal to ______.
