Question

2. Kate and Nora each have a sum of money. The ratio of the amount of money
Kate has to that of Nora is 3:5. After Nora gives $150 to Kate, the ratio of
the amount of money Kate has to that of Nora becomes 7:9. Find the sum
of money Kate had initially.
​

Answer 1

Answer:-

Given:-

Amounts of money with Kate and Nora are in the ratio 3 : 5.

Let,

• Amount of money with Kate = Rs. 3x
• Amount of money with Nora = Rs. 5x

Also given that,

If Nora gives Rs. 150 to Kate, the ratio becomes 7 : 9.

According to the above condition;

$\implies \sf \: \frac{3x + 150}{5x - 150} = \frac{7}{9} \\ \\ \\ \implies \sf \:9(3x + 150) = 7(5x - 150) \\ \\ \\ \implies \sf \:27x + 1350 = 35x - 1050\\ \\ \\ \implies \sf \:1350 + 1050 = 35x - 27x \\ \\ \\ \implies \sf \:2400 = 8x \\ \\ \\ \implies \sf \: \frac{2400}{8} = x \\ \\ \\ \implies \boxed{\sf Rs. \: 300 = x}$

Hence;

Amount of money with Kate = 3x = 3(300) = Rs. 900

∴ Kate initially had Rs. 900.

Answer 2

Answer:

Given :-

• Kate and Nora each have a sum of money. The ratio of the amount of money Kate has to that of Nora is 3 : 5. After Nora gives Rs 150 to Kate, the ratio of money Kate has to that of Nora become 7 : 9.

To Find :-

• What is the sum of money Kate had initially.

Solution :-

Let, the sum of money Kate had initially be Rs 3x

And, the Nora sum of money will be Rs 5x

According to the question,

↦ $\sf \dfrac{3x + 150}{5x - 150} =\: \dfrac{7}{9}$

↦ $\sf 7(5x - 150) =\: 9(3x + 150)$

↦ $\sf 35x - 1050 =\: 27x + 1350$

↦ $\sf 35x - 27x =\: 1350 + 1050$

↦ $\sf 8x =\: 2400$

↦ $\sf x =\: \dfrac{\cancel{2400}}{\cancel{8}}$

➠ $\sf\bold{\pink{x =\: Rs\: 300}}$

Hence, the required money get Kate and Nora are :

➲ Sum of money Kate had initially :

↦ $\sf Rs\: 3x$

↦ $\sf Rs\: 3(300)$

↦ $\sf Rs\: 3 \times 300$

➠ $\sf\bold{\red{Rs\: 900}}$

And,

➲ Sum of money Nora had initially :

↦ $\sf Rs\: 5x$

↦ $\sf Rs\: 5(300)$

↦ $\sf Rs\: 5 \times 300$

➠ $\sf\bold{\red{Rs\: 1500}}$

$\therefore$ The sum of money Kate had initially is Rs 900 .