Question

Two numbers T1 and T2 are such that the sum of 50 percent of T1 and 20 percent of T2 is 5/3 of the sum of 15 percent of T1 and 18 percent of T2. What is the respective ratio of T1 and T2?​

Answer 1

Answer:

2:5

Step-by-step explanation:

For convenience, let T1 = a,  T2 = b.

According to the question, sum of 50 % of a and 20 % of b is 5/3 of the sum of 15 % of a and 18 % of b.

   Note that:

50% of a = (50/100) x a = (0.5)a

20% of b = (20/100) x b = (0.2)b

15% of a = (15/100) x a = (0.15)a

18% of b = (18/100) x b = (0.18)b

Here,

⇒ 50% a + 20% b = (5/3) [15% a + 18% b]

⇒ 0.5a + 0.2b = (5/3) [0.15a + 0.18b]

⇒ 3(0.5a + 0.2b) = 5(0.15a + 0.18b)

⇒ 1.5a + 0.6b = 0.75a + 0.9b

⇒ 1.5a - 0.75a = 0.9b - 0.6b

⇒ 0.75a = 0.3b

⇒ a/b = 0.3/0.75 = 30/75

⇒ a/b = 2/5

⇒ T1/T2 = 2/5

Ratio of T1 and T2 is 2:5

Answer 2

Given :-

There are Two numbers T1 and T2 are such that the sum of 50 percent of T1 and 20 percent of T2 is 5/3 of the sum of 15 percent of T1 and 18 percent of T2

To Find :-

Ratio of T1 and T2

Solution :-

Let

T1 = x

T2 = y

$\sf 50\% \times x = \dfrac{50}{100} = 0.5x$

$\sf 20\% \times y = \dfrac{20}{100} \times y = 0.2y$

$\sf 15\% \times x = \dfrac{15}{100} \times x= 0.15x$

$\sf 18\% \times y = \dfrac{18}{100}\times y = 0.18y$

Now,

50% x + 20% y = (5/3) (15% x + 18% y)

3(0.5x + 0.2y) = 5(0.15x + 0.18y)

(1.5x + 0.6y) = (0.75x + 0.9y)

0.75a = 0.30b

a/b = 0.75/0.30

a/b = 2/5