Central Tendency & DispersionMTP June 2023 Series IIQuestion 2920 of 473
All Questions

The average of 6\displaystyle 6 numbers is 30\displaystyle 30. If the average of the first four is 25\displaystyle 25 and that of the last three is 35\displaystyle 35, the fourth number is

Options

A25
B30
C35
D40
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Correct Answer

✅ Option a — 25

All Options:

  • A25
  • B30
  • C35
  • D40

Detailed Solution & Explanation

**Step 1: Find the total sum of all 6 numbers.** Sum of all 6=6×30=180\text{Sum of all 6} = 6 \times 30 = 180 **Step 2: Find sum of first 4 numbers.** Sum of first 4=4×25=100\text{Sum of first 4} = 4 \times 25 = 100 **Step 3: Find sum of last 3 numbers.** Sum of last 3=3×35=105\text{Sum of last 3} = 3 \times 35 = 105 **Step 4: Find the 4th number.** Note: The 6 numbers are n1,n2,n3,n4,n5,n6\displaystyle n_1, n_2, n_3, n_4, n_5, n_6. - First 4: n1+n2+n3+n4=100\displaystyle n_1+n_2+n_3+n_4 = 100 - Last 3: n4+n5+n6=105\displaystyle n_4+n_5+n_6 = 105 - All 6: n1+n2+n3+n4+n5+n6=180\displaystyle n_1+n_2+n_3+n_4+n_5+n_6 = 180 Adding first 4 and last 3: (n1+n2+n3+n4)+(n4+n5+n6)=100+105=205(n_1+n_2+n_3+n_4) + (n_4+n_5+n_6) = 100 + 105 = 205 But total sum =180\displaystyle = 180, so: 205−n4=180  ⟹  n4=205−180=25205 - n_4 = 180 \implies n_4 = 205 - 180 = 25 Hence, **Option A** is the correct answer.

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