# CAT 2019 Set-1 | Question: 68

629 views

The income of Amala is $20\%$ more than that of Bimala and $20\%$ less than that of Kamala. If Kamala's income goes down by $4\%$ and Bimala’s goes up by $10\%$, then the percentage by which Kamala's income would exceed Bimala’s is nearest to

1. $31$
2. $28$
3. $32$
4. $29$

Let the income of Bimala $= 100x$

The income of Amala is $20\%$ more than that of Bimala.

So, the income of Amala $= 100x \times \frac{120}{100} = 120x$

The ratio of Bimala and Amala $= 100x : 120x = 5:6 \quad \longrightarrow (1)$

Let the income of Kamala $= 100y$

The income of Amala $20\%$ less than that of Kamala.

So, the income of Amala $= 100y \times \frac{80}{100} = 80x$

The ratio fo Kamala and Amala $= 100y : 80y = 5:4 \quad \longrightarrow (2)$

Now, combining equation $(1)$ and $(2)$, we get

• Bimala : Amala $= (5 : 6) \times 4 = 20: 24$
• Kamala : Amala $= (5 : 4) \times 6 = 30: 24$

The ratio of Bimala : Amala : Kamala $= 20 : 24 : 30 = 10 : 12 : 15$

If Kamala's income goes down by $4\%$ and Bimala’s goes up by $10\%$. Then,

• Kamala’s income $= 15 \times \frac{96}{100} = 14 . 4$
• Bimala’s income $= 10 \times \frac {110}{100} = 11$

$\therefore$ The percentage by which kamala’s income would exceed Bimala’s income $= \frac {(14 . 4 – 11)}{11} \times 100 = \frac {3 .4}{11} \times 100 = 30 . 90 \approx 31.$

Correct Answer$: \text{A}$

In a class, $60\%$ of the students are girls and the rest are boys. There are $30$ more girls than boys. If $68\%$ of the students, including $30$ boys, pass an examinati...
Meena scores $40\%$ in an examination and after review, even though her score is increased by $50\%$, she fails by $35$ marks. If her post-review score is increased by $2... 2 votes 1 answer 3 780 views If$m$and$n$are integers such that$(\sqrt{2})^{19}3^{4}4^{2}9^{m}8^{n}=3^{n}16^{m}(\sqrt[4]{64})$then$m$is$-20$$-12$$-24$$-16 1 votes 1 answer 4 614 views On selling a pen at 5\% loss and a book at 15\% gain, Karim gains Rs. 7. If he sells the pen at 5\% gain and the book at 10\% gain, he gains Rs. 13. What is t... 1 votes 1 answer 5 819 views Corners are cut off from an equilateral triangle T to produce a regular hexagon H. Then, the ratio of the area of H to the area of T is 5:6$$4:5$$3:4$$2:3\$