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IBPS PO Mains 30 Nov 2024 Shift 2 Paper

Question Numbers: 134-137

Directions: Read the following information carefully and answer the questions based on it.

There are three sellers – Arun, Binny, and Chanda – dealing in hats and caps.

The number of hats sold by Binny is x% more than the number of caps sold by Arun. The total items (hats + caps) sold by Arun are 50% higher than the number of caps sold by him. The ratio of Binny’s caps to Chanda’s hats is 7 : 5. The number of caps sold by Chanda is 20% less than the caps sold by Arun. The total sales of Chanda (hats + caps) equals (Y × Binny’s hats) + 1. Chanda’s caps are also 36 more than Arun’s hats. The average number of hats sold by Arun and Chanda is 80. Altogether, Arun, Binny, and Chanda sold 672 hats and caps.

Question : 134 of 155

Marks: +1, -0

What is the average of the caps sold by Binny and Chanda?

Validate

Solution:

Concept:

Use the given relationships between hats and caps sold by Arun, Binny, and Chanda to find the caps sold by Binny and Chanda, then calculate their average.

Explanation:

Let

H_A

and

C_A

be Arun's hats and caps,

H_B

and

C_B

be Binny's hats and caps, and

H_C

and

C_C

be Chanda's hats and caps.

Given:

H_A + C_A = 1.5 \times C_A

So,

H_A = 0.5 \times C_A

Also,

C_C = 0.8 \times C_A

and

C_C = H_A + 36

Substitute

H_A = 0.5 C_A

into

C_C = H_A + 36

0.8 C_A = 0.5 C_A + 36

0.3 C_A = 36

C_A = 120

Therefore,

H_A = 0.5 \times 120 = 60

and

C_C = 0.8 \times 120 = 96

Average of Arun's and Chanda's hats is 80:

\frac{H_A + H_C}{2} = 80

60 + H_C = 160

H_C = 100

Given

C_B : H_C = 7 : 5

\frac{C_B}{100} = \frac{7}{5}

C_B = 140

Total items sold

= 672

(H_A + C_A) + (H_B + C_B) + (H_C + C_C) = 672

(60 + 120) + (H_B + 140) + (100 + 96) = 672

H_B + 516 = 672

H_B = 156

Using

H_B = C_A\left(1 + \frac{x}{100}\right)

156 = 120\left(1 + \frac{x}{100}\right)

1.3 = 1 + \frac{x}{100}

x = 30

Using

H_C + C_C = Y \times H_B + 1

100 + 96 = 156Y + 1

195 = 156Y

Y = 1.25

Now, Binny's caps

= 140

and Chanda's caps

= 96

Average

= \frac{140 + 96}{2} = \frac{236}{2} = 118

Answer:

118

(Option B)

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