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CAT 2017 Slot 1 — QA Question 8

RatioEasy

Suppose, C1, C2, C3, C4, and C5 are five companies. The profits made by C1, C2, and C3 are in the ratio 9 : 10 : 8 while the profits made by C2, C4, and C5 are in the ratio 18 : 19 : 20. If C5 has made a profit of Rs 19 crore more than C1, then the total profit (in Rs) made by all five companies is:

Answer & solution

Correct answer: 438 crore

  • 438 crore

  • B

    435 crore

  • C

    348 crore

  • D

    345 crore

Solution

Easy

The two ratio chains share C2C_2. Scale them to a common C2C_2 value, express every company's profit in one variable xx, then use C5−C1=19C_5-C_1=19 to fix xx and add everything up.

1

Link the chains through C2C_2. First chain C1:C2:C3=9:10:8C_1:C_2:C_3 = 9:10:8; second C2:C4:C5=18:19:20C_2:C_4:C_5 = 18:19:20. Make C2C_2 common by scaling the first chain by 99 (so C2=90C_2=90) and the second by 55 (so C2=90C_2=90).

C1:C2:C3=81:90:72(×9)C2:C4:C5=90:95:100(×5)\begin{aligned} &C_1:C_2:C_3 = 81:90:72 \quad\text{(}\times 9\text{)}\\ &C_2:C_4:C_5 = 90:95:100 \quad\text{(}\times 5\text{)} \end{aligned}
2

One variable for all five. Let the common unit be xx.

C1=81x, C2=90x, C3=72x, C4=95x, C5=100x\begin{aligned} &C_1=81x,\ C_2=90x,\ C_3=72x,\ C_4=95x,\ C_5=100x \end{aligned}
3

Use C5−C1=19C_5-C_1=19 crore.

100x−81x=19⇒ 19x=19⇒x=1\begin{aligned} &100x - 81x = 19\\ &\Rightarrow\ 19x = 19 \Rightarrow x = 1 \end{aligned}
4

Total profit. Add the five.

(81+90+72+95+100)x=438x⇒ 438×1=438 crore\begin{aligned} &(81+90+72+95+100)x = 438x\\ &\Rightarrow\ 438\times 1 = 438 \text{ crore} \end{aligned}
Rs 438 crore\text{Rs }438\text{ crore}

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CAT 2017 Slot 1 QA Q8: Suppose, C 1 , C 2 , C 3 , C 4 , and C 5 are five companies. The profits made by C 1 , C 2 , and C 3 are in th — Solution | TheCATExam