Question

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

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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.

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What is the sum of money Kate had initially?

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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,

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

$↦ \sf 7(5x - 150) =\: 9(3x + 150)7(5x−150)=9(3x+150)$

$↦ \sf 35x - 1050 =\: 27x + 135035x−1050=27x+1350$

$↦ \sf 35x - 27x =\: 1350 + 105035x−27x=1350+1050$

$↦ \sf 8x =\: 24008x=2400$

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

$➠ \sf\bold{\pink{x =\: Rs\: 300}}x=Rs300$

Hence, the required money get Kate and Nora are :

➲ Sum of money Kate had initially :

$↦ \sf Rs\: 3xRs3x$

$↦ \sf Rs\: 3(300)Rs3(300)$

$↦ \sf Rs\: 3 \times 300Rs3×300$

$➠ \sf\bold{\red{Rs\: 900}}Rs900$

And,

➲ Sum of money Nora had initially :

$↦ \sf Rs\: 5xRs5x$

$↦ \sf Rs\: 5(300)Rs5(300)$

$↦ \sf Rs\: 5 \times 300Rs5×300$

$➠ \sf\bold{\red{Rs\: 1500}}Rs1500$

∴ The sum of money Kate had initially is Rs 900.