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Percentage Salary Hikes and Ratios

CAT 2023 Slot 1 · Quantitative Ability · Easy · Arithmetic

This is an easy Quantitative Ability question from the CAT 2023 Slot 1 paper. It tests Arithmetic. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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The salaries of three friends Sita, Gita and Mita are initially in the ratio 5 : 6 : 7, respectively. In the first year, they get salary hikes of 20%, 25% and 20%, respectively. In the second year, Sita and Mita get salary hikes of 40% and 25%, respectively, and the salary of Gita becomes equal to the mean salary of the three friends. The salary hike of Gita in the second year is

  1. A.

    26%

  2. B.

    28%

  3. C.

    25%

  4. D.

    30%

Answer

A

Explanation

Initial salaries: S0=50,G0=60,M0=70S_0 = 50, G_0 = 60, M_0 = 70.

Year 1:

  • S1=50×1.20=60S_1 = 50 \times 1.20 = 60
  • G1=60×1.25=75G_1 = 60 \times 1.25 = 75
  • M1=70×1.20=84M_1 = 70 \times 1.20 = 84

Year 2:

  • S2=60×1.40=84S_2 = 60 \times 1.40 = 84
  • M2=84×1.25=105M_2 = 84 \times 1.25 = 105
  • Let Gita's salary in year 2 be G2G_2.

G2=S2+G2+M23  ⟹  2G2=S2+M2=84+105=189  ⟹  G2=94.5G_2 = \frac{S_2 + G_2 + M_2}{3} \implies 2 G_2 = S_2 + M_2 = 84 + 105 = 189 \implies G_2 = 94.5.

Percentage hike for Gita in 2nd year =94.5−7575×100%=19.575×100%=26%= \frac{94.5 - 75}{75} \times 100\% = \frac{19.5}{75} \times 100\% = 26\%.

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