SNAP questions on Arithmetic - Average

Asked: the number of women.

Let there be \( m \) men and \( w \) women.

\( m + w = 160 \)

\( 7m + 12w = 1240 \)

Shortcut: if all 160 were men, they would get \( 160 \times 7 = 1120 \) apples. The extra \( 1240 - 1120 = 120 \) apples come from women, and each woman gets \( 12 - 7 = 5 \) more than a man.

\( w = \frac{120}{5} = 24 \)

Check: 136 men × 7 = 952 and 24 women × 12 = 288. Total 952 + 288 = 1240.

Answer: 24

Asked: the largest of four different natural numbers.

Intended working: let the largest number be L. Take "the average of the first three is 32" to mean that the other three numbers add up to 96.

Average of all four \( = \frac{L + 96}{4} \).

One-fourth of this average is 24 less than L:

\( \frac{L + 96}{16} = L - 24 \)

\( L + 96 = 16L - 384 \)

\( 15L = 480 \), so \( L = 32 \).

Caution: this does not fit the other conditions. If the largest number is 32, the other three distinct natural numbers are each 31 or less, so their sum is at most 31 + 30 + 29 = 90. It cannot be 96. If instead "first three" means the three largest (L included), the fourth number is unknown and L cannot be found.

The memory-based version of this question has probably lost a detail. 32 is the value the question intends.

Answer: 32 (intended), but the data as recalled are inconsistent.

Asked: the amount each friend paid.

There are 25 people in all: Aman and 24 friends. Let each friend pay x.

Total paid = 24x + 290.

The average is ₹10 more than x, so the total is also 25(x + 10).

\( 24x + 290 = 25x + 250 \)

x = 40.

Faster method: each of the 24 friends pays ₹10 below the average. Their combined shortfall of 24 × 10 = ₹240 must be covered by Aman, so Aman pays the average plus 240.

Average = 290 − 240 = 50, so each friend pays 50 − 10 = 40.

Check: total = 24 × 40 + 290 = 1250, and 1250/25 = 50, which is 40 + 10.

Answer: Rs. 40

Asked: the corrected mean.

Recorded total \( = 50 \times 62 = 3100 \).

Wrong values used: 75 + 7 = 82.

Correct values: 57 + 70 = 127.

Corrected total \( = 3100 - 82 + 127 = 3145 \).

Correct mean \( = \frac{3145}{50} = 62.90 \).

Faster method: the total rises by 45, so the mean rises by \( \frac{45}{50} = 0.9 \). That gives 62 + 0.9 = 62.9.

Answer: 62.90