# Exercise : 3

(b) 20, 20, 18

(c) 18, 22, 20

(d) 21, 20, 19

(e) None of the above

**Ans.a**

Given A + B = 40…(i)

C + B = 38 … (ii)

A + C = 42…(iii)

(i) + (ii) + (iii) ⇒ A + B + C = 60 …(iv)

from (i) and (iv), we get

C = 20 years

∴ B = 18 years and A = 22 years

(b) 2 years

(c) 1

^{1}⁄

_{2}years

(d) cannot be determined

(e) None of the above

**Ans.b**

Sum of present ages of the six members

= (17 × 6) years = 102 years.

Sum of present ages of the 5 members (excluding baby)

= 5 × (17 + 3) years = 100 years.

∴ Age of the baby = 102 – 100 = 2 years

(b) 18

(c) 22

(d) 19

(e) None of the above

**Ans.a**

Let the number of persons, initially going for Picnic = x

∴ Sum of their ages = 16x

Also, \(\frac{16x + 15 \times 20}{x + 20}\) = 15.5

⇒ 0.5x = 10 ⇒ x = 20 years.

(b) 43

(c) 44

(d) 45

(e) None of the above

**Ans.b**

Let ‘x’ be the average score after 12 th innings

⇒ 12x = 11 × (x – 2) + 65

∴ x = 43

(b) 20

(c) 40

(d) 73

(e) None of the above

**Ans.c**

Let there be x pupils in the class.

Total increase in marks = (x × ^{1}⁄_{2}) = ^{x}⁄_{2}.

∴ ^{x}⁄_{2} = (83 - 63) ⇒ ^{x}⁄_{2} = 20 ⇒ x = 40.

(b) 6.50

(c) 6.75

(d) 7.00

(e) None of the above

**Ans.a**

Total runs in the first 10 overs

= 10 × 3.2 = 32

Run rate required in the remaining 40 overs

= \(\frac{282 - 32}{40} = \frac{250}{40} = 6.25\) runs per over.

(b) 4

(c) 840

(d) 90

(e) None of the above

**Ans.b**

Remaining pages = 512 – 302 = 210

Let average printing error in remaining pages = x

Then, \(\frac{1208 + 210 \times x}{512} = 4\)

⇒ 210x = 840 ⇒ x = 4

(b) 40

(c) 38

(d) 36

(e) None of the above

**Ans.b**

Attendance on the fifth day = 32 × 5 – 30 × 4

= 160 – 120 = 40

(b) 72

(c) 75

(d) 78

(e) None of the above

**Ans.d**

Income of 6 months = (6 × 85) – debt

= 510 – debt

Income of the man for next 4 months

= 4 × 60 + debt + 30

= 270 + debt

∴ Income of 10 months = 780

Average monthly income = 780 ÷ 10 = 78

(b) 173

(c) 174

(d) 175

(e) None of the above

**Ans.c**

Total runs = 40 × 50 = 2000

Let his highest score be = x

Then his lowest score = x – 172

Now \(\frac{200 - x - \left(x - 172 \right)}{38} = 48\)

⇒ 2x = 2172 – 1824

⇒ x = 174