1. If x:y=3:5,find the ratio 3x+4y:8x+5y.
2. If x:y=8:9 find the ratio (7x−4y):3x+2y
3. If two numbers are in the ratio 6:13 and their l.c.m. is 312, find the numbers.
4. What should be added to each term of the ratio 7:13 so that the ratio becomes 2:3
1). Let x=3λ
y=5λ
So, 3x+4y3x+5y=3(3λ)+4(5λ)8(3λ)+5(5λ)=9λ+20λ24λ+25λ
=29λ49λ=29:49
2). Let x=8λ
y=9λ
So, 7x−4y3x+2y=7(8λ)−4(9λ)3(8λ)+2(9λ)=56λ−36λ24λ+18λ=20λ42λ=1021=10:21
3). Let the numbers be 6x and 13x
Now, Since ′x′ is a common multiple
∴ LCM of 6x and 13x=13×6×x
=78x
Now, 78x=312⇒x=31278=4
Hence, Required numbers are ⇒6x=6×4=24
13x=13×4=52
4). Let the number to be added by y
Such that, 7+y13+y=213⇒21+3y=26+2y⇒y=5