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CAT 2021 Slot 1 — QA Question 3

RatioEasy

The amount Neeta and Geeta together earn in a day equals what Sita alone earns in 6 days. The amount Sita and Neeta together earn in a day equals what Geeta alone earns in 2 days. The ratio of the daily earnings of the one who earns the most to that of the one who earns the least is

Answer & solution

  • A

    7 : 3

  • B

    3 : 2

  • 11 : 3

  • D

    11 : 7

Solution

Easy

Call the daily earnings n,g,sn,g,s. Translate each "earns in kk days" statement into a linear equation, eliminate variables to express everything as a multiple of ss, then take the largest-to-smallest ratio.

1

Translate both statements. "Neeta and Geeta together in a day == Sita in 6 days" and "Sita and Neeta together in a day == Geeta in 2 days".

n+g=6s...(1)n+s=2g...(2)\begin{aligned} &n+g=6s \quad\text{...(1)}\\ &n+s=2g \quad\text{...(2)} \end{aligned}
2

Eliminate nn to find gg. From (1), n=6s−gn=6s-g; substitute into (2).

(6s−g)+s=2g(sub n=6s−g into (2))⇒ 7s=3g⇒ g=7s3...(3)\begin{aligned} &(6s-g)+s=2g \quad\text{(sub }n=6s-g\text{ into (2))}\\ &\Rightarrow\ 7s=3g\\ &\Rightarrow\ g=\tfrac{7s}{3} \quad\text{...(3)} \end{aligned}
3

Find nn. Substitute (3) back into (1).

n=6s−g=6s−7s3(from (1),(3))⇒ n=18s−7s3=11s3\begin{aligned} &n=6s-g=6s-\tfrac{7s}{3} \quad\text{(from (1),(3))}\\ &\Rightarrow\ n=\tfrac{18s-7s}{3}=\tfrac{11s}{3} \end{aligned}
4

Order them and take the ratio. Comparing the three in terms of ss.

n=11s3> g=7s3> s(so Neeta most, Sita least)⇒ mostleast=11s/3s=113\begin{aligned} &n=\tfrac{11s}{3}>\ g=\tfrac{7s}{3}>\ s \quad\text{(so Neeta most, Sita least)}\\ &\Rightarrow\ \frac{\text{most}}{\text{least}}=\frac{11s/3}{s}=\frac{11}{3} \end{aligned}
Ratio=11:3(option (c))\text{Ratio}=11:3 \quad\text{(option (c))}
CAT 2021 Slot 1 QA Q3: The amount Neeta and Geeta together earn in a day equals what Sita alone earns in 6 days. The amount Sita and — Solution | TheCATExam