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Page 1
NTSE STAGE – I (DELHI STATE)
05 – A (2018 – 19)
(For Class – X)
MENTAL ABILITY TEST (MAT)
HINTS & SOLUTIONS
1. 4
1. ? ?
2
2
25
x 10 x 10x 25 0 x 5 0 x 5
x
? ? ? ? ? ? ? ? ? ? ?
2
2
50 50
25 25 2 27
25
x
x
? ?? ?? ?
2. 1
2. x + y = 3, x
2
+ y
2
= 15
(x – y)
2
= ?, (x
2
+ y
2
+ 2xy) = 9 ? 15 + 2xy = 9
? xy = ?3
(x – y)
2
= x
2
+ y
2
– 2xy = 15 + 6 = 21
3. 2
3.
a b c
K a 3K,b 5K,c 7K
357
??? ? ? ? ?
a b c 3K 5K 7K
3
b 5K
? ? ? ?
? ? ?
4. 3
4. x + y = 25, x
2
+ y
2
= 425
? x
2
+ y
2
+ 2xy = 625
? 425 + 2xy = 625 ? xy = 100
5. 1
5.
2
0.64 a 64 ? ?
2
2
0.64 1 1
64 a a 0.1
100 10 a
? ? ? ? ? ? ?
6. 2
6. Dividend = divisor × quotient + remainder
Divisor = 30 × q
Divisor = 4 × r
? q = 20 ? Divisor ? 600 & remainder
600
150
4
? ?
Dividend 600 20 150 12,150 ? ? ? ? ?
7. 4
7. 3
a-2b
= 27 ?3
a – 2b
= 3
3
? a – 2b = 3 …(1)
9
a+b
= 3 ? 3
2a + 2b
= 3
1
? 2a + 2b = 1 …(2)
by equation (1) and (2)
5 4
3a 4 a ,b
3 6
? ? ? ? ?
?
4 / 3
a 8
b 5
5 / 6
? ?
? ? ? ?
? ?
?
? ?
8. 4
Page 2
NTSE STAGE – I (DELHI STATE)
05 – A (2018 – 19)
(For Class – X)
MENTAL ABILITY TEST (MAT)
HINTS & SOLUTIONS
1. 4
1. ? ?
2
2
25
x 10 x 10x 25 0 x 5 0 x 5
x
? ? ? ? ? ? ? ? ? ? ?
2
2
50 50
25 25 2 27
25
x
x
? ?? ?? ?
2. 1
2. x + y = 3, x
2
+ y
2
= 15
(x – y)
2
= ?, (x
2
+ y
2
+ 2xy) = 9 ? 15 + 2xy = 9
? xy = ?3
(x – y)
2
= x
2
+ y
2
– 2xy = 15 + 6 = 21
3. 2
3.
a b c
K a 3K,b 5K,c 7K
357
??? ? ? ? ?
a b c 3K 5K 7K
3
b 5K
? ? ? ?
? ? ?
4. 3
4. x + y = 25, x
2
+ y
2
= 425
? x
2
+ y
2
+ 2xy = 625
? 425 + 2xy = 625 ? xy = 100
5. 1
5.
2
0.64 a 64 ? ?
2
2
0.64 1 1
64 a a 0.1
100 10 a
? ? ? ? ? ? ?
6. 2
6. Dividend = divisor × quotient + remainder
Divisor = 30 × q
Divisor = 4 × r
? q = 20 ? Divisor ? 600 & remainder
600
150
4
? ?
Dividend 600 20 150 12,150 ? ? ? ? ?
7. 4
7. 3
a-2b
= 27 ?3
a – 2b
= 3
3
? a – 2b = 3 …(1)
9
a+b
= 3 ? 3
2a + 2b
= 3
1
? 2a + 2b = 1 …(2)
by equation (1) and (2)
5 4
3a 4 a ,b
3 6
? ? ? ? ?
?
4 / 3
a 8
b 5
5 / 6
? ?
? ? ? ?
? ?
?
? ?
8. 4
8. 17 x 11 11 6 2. 11. 6 ? ? ? ?
x 2 6 ? ?
2
x 24 ? ?
9. 1
9. 0.02 0.2 a 0.2 0.2 b ?? ? ??
0.02 0.2 a 0.2 0.2 0.2 0.2 b ? ? ? ? ????
a 0.2 0.2 0.2
0.4
b 0.02
? ?
? ? ?
10. 1
10. 7 3, 7 3 ? ? ? ? ? ?
14, 46 ? ? ?? ???
2
x 14x 46 0 ? ? ? ?
11. 2
11. Q = 3R = 2(P + R)
Q = 2P + 2R
3R = 2P + 2R
R = 2P
? Q = 2P + 4P = 6P
? P + 6P + 2P = 180° ? 9P = 180° ? P = 20°
? Q = 6 × 20 = 120°
12. 2
12. ? ? ? ?
p x 3
,p x 3K,q x 3K
q x 3
?
? ? ? ? ?
?
? ? ? ?
? ? ? ?
2 2
2 2
2 2 2 2
x 3K x 3K
p q
p q
x 3K x 3K
? ? ? ? ? ? ?
?
? ? ? ?
?
?
? ? ? ? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ?
2 2
2 2
x 3 x 3
x 3 x 3
? ? ?
?
? ? ?
? ? ? ?
? ?
2
x3 x 3 x 3 x3
2 x 9
?? ? ???
?
?
? ?
2
2x 6
2 x 9
?
?
?
2
6x
x 9
?
?
13. 1
13. Perimeter of square = 4a = 2(l + b)
l = 24 = 2b ? b = 12
? 4a = 72 ? a = 18
? Area of square = 18
2
= 324
14. 1
14.
2
1 1
1 1 1
2
2 2 2
2 2
1
r h
V h h 2 1 8
3
1
V 3 4 h h 3
r h
3
?
? ? ? ? ? ?
?
Page 3
NTSE STAGE – I (DELHI STATE)
05 – A (2018 – 19)
(For Class – X)
MENTAL ABILITY TEST (MAT)
HINTS & SOLUTIONS
1. 4
1. ? ?
2
2
25
x 10 x 10x 25 0 x 5 0 x 5
x
? ? ? ? ? ? ? ? ? ? ?
2
2
50 50
25 25 2 27
25
x
x
? ?? ?? ?
2. 1
2. x + y = 3, x
2
+ y
2
= 15
(x – y)
2
= ?, (x
2
+ y
2
+ 2xy) = 9 ? 15 + 2xy = 9
? xy = ?3
(x – y)
2
= x
2
+ y
2
– 2xy = 15 + 6 = 21
3. 2
3.
a b c
K a 3K,b 5K,c 7K
357
??? ? ? ? ?
a b c 3K 5K 7K
3
b 5K
? ? ? ?
? ? ?
4. 3
4. x + y = 25, x
2
+ y
2
= 425
? x
2
+ y
2
+ 2xy = 625
? 425 + 2xy = 625 ? xy = 100
5. 1
5.
2
0.64 a 64 ? ?
2
2
0.64 1 1
64 a a 0.1
100 10 a
? ? ? ? ? ? ?
6. 2
6. Dividend = divisor × quotient + remainder
Divisor = 30 × q
Divisor = 4 × r
? q = 20 ? Divisor ? 600 & remainder
600
150
4
? ?
Dividend 600 20 150 12,150 ? ? ? ? ?
7. 4
7. 3
a-2b
= 27 ?3
a – 2b
= 3
3
? a – 2b = 3 …(1)
9
a+b
= 3 ? 3
2a + 2b
= 3
1
? 2a + 2b = 1 …(2)
by equation (1) and (2)
5 4
3a 4 a ,b
3 6
? ? ? ? ?
?
4 / 3
a 8
b 5
5 / 6
? ?
? ? ? ?
? ?
?
? ?
8. 4
8. 17 x 11 11 6 2. 11. 6 ? ? ? ?
x 2 6 ? ?
2
x 24 ? ?
9. 1
9. 0.02 0.2 a 0.2 0.2 b ?? ? ??
0.02 0.2 a 0.2 0.2 0.2 0.2 b ? ? ? ? ????
a 0.2 0.2 0.2
0.4
b 0.02
? ?
? ? ?
10. 1
10. 7 3, 7 3 ? ? ? ? ? ?
14, 46 ? ? ?? ???
2
x 14x 46 0 ? ? ? ?
11. 2
11. Q = 3R = 2(P + R)
Q = 2P + 2R
3R = 2P + 2R
R = 2P
? Q = 2P + 4P = 6P
? P + 6P + 2P = 180° ? 9P = 180° ? P = 20°
? Q = 6 × 20 = 120°
12. 2
12. ? ? ? ?
p x 3
,p x 3K,q x 3K
q x 3
?
? ? ? ? ?
?
? ? ? ?
? ? ? ?
2 2
2 2
2 2 2 2
x 3K x 3K
p q
p q
x 3K x 3K
? ? ? ? ? ? ?
?
? ? ? ?
?
?
? ? ? ? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ?
2 2
2 2
x 3 x 3
x 3 x 3
? ? ?
?
? ? ?
? ? ? ?
? ?
2
x3 x 3 x 3 x3
2 x 9
?? ? ???
?
?
? ?
2
2x 6
2 x 9
?
?
?
2
6x
x 9
?
?
13. 1
13. Perimeter of square = 4a = 2(l + b)
l = 24 = 2b ? b = 12
? 4a = 72 ? a = 18
? Area of square = 18
2
= 324
14. 1
14.
2
1 1
1 1 1
2
2 2 2
2 2
1
r h
V h h 2 1 8
3
1
V 3 4 h h 3
r h
3
?
? ? ? ? ? ?
?
15. 3
15. 2
x
= 8
y – 1
? x = 3y – 3 …(1)
9
y
= 3
x – 6
? 2y = x – 6 …(2)
by (1) & (2)
x = 24, y = 9
? x + y = 33
16. 1
16. x – y : (x + y) : xy = 1 : 7 : 24
x y 1
7x 7y x y
x y 7
?
? ? ? ? ?
?
= 6x = 8y
4
x y
3
? ?
2
4
y y
x y 1y 1 1
3
y 6
4
xy 4y 24 4y
y y
3
?
?
? ? ? ? ? ?
?
4
x 6 8
3
? ? ? ?
? xy = 48
17. 1
17. 6, 7, 7, 7, 9, 9, 14, 15
mode = 7
range = 15 – 6 = 9
median = 8
798
mean 8
3
? ?
? ? ?
18. 4
18. Let initial income be x
? initial expenditure = 0.8 x
New expenditure = 1.375 (0.8 x)
= 1.1 x
New income
7x
6
?
? Saving
7x 11x
6 10
? ?
2x x
30 15
? ?
x
5
15
present percent saving 100 5 %
7x
7
6
? ? ? ?
19. 3
19. Let the cost of 1 chair be ‘c’ and the cost of 1 table be ‘t’
5c + 3t = 3110
c = t – 210
So, we get,
5t – 1050 + 3t = 3110 ? 8t = 4160 ? t = 520
? c = 310
Page 4
NTSE STAGE – I (DELHI STATE)
05 – A (2018 – 19)
(For Class – X)
MENTAL ABILITY TEST (MAT)
HINTS & SOLUTIONS
1. 4
1. ? ?
2
2
25
x 10 x 10x 25 0 x 5 0 x 5
x
? ? ? ? ? ? ? ? ? ? ?
2
2
50 50
25 25 2 27
25
x
x
? ?? ?? ?
2. 1
2. x + y = 3, x
2
+ y
2
= 15
(x – y)
2
= ?, (x
2
+ y
2
+ 2xy) = 9 ? 15 + 2xy = 9
? xy = ?3
(x – y)
2
= x
2
+ y
2
– 2xy = 15 + 6 = 21
3. 2
3.
a b c
K a 3K,b 5K,c 7K
357
??? ? ? ? ?
a b c 3K 5K 7K
3
b 5K
? ? ? ?
? ? ?
4. 3
4. x + y = 25, x
2
+ y
2
= 425
? x
2
+ y
2
+ 2xy = 625
? 425 + 2xy = 625 ? xy = 100
5. 1
5.
2
0.64 a 64 ? ?
2
2
0.64 1 1
64 a a 0.1
100 10 a
? ? ? ? ? ? ?
6. 2
6. Dividend = divisor × quotient + remainder
Divisor = 30 × q
Divisor = 4 × r
? q = 20 ? Divisor ? 600 & remainder
600
150
4
? ?
Dividend 600 20 150 12,150 ? ? ? ? ?
7. 4
7. 3
a-2b
= 27 ?3
a – 2b
= 3
3
? a – 2b = 3 …(1)
9
a+b
= 3 ? 3
2a + 2b
= 3
1
? 2a + 2b = 1 …(2)
by equation (1) and (2)
5 4
3a 4 a ,b
3 6
? ? ? ? ?
?
4 / 3
a 8
b 5
5 / 6
? ?
? ? ? ?
? ?
?
? ?
8. 4
8. 17 x 11 11 6 2. 11. 6 ? ? ? ?
x 2 6 ? ?
2
x 24 ? ?
9. 1
9. 0.02 0.2 a 0.2 0.2 b ?? ? ??
0.02 0.2 a 0.2 0.2 0.2 0.2 b ? ? ? ? ????
a 0.2 0.2 0.2
0.4
b 0.02
? ?
? ? ?
10. 1
10. 7 3, 7 3 ? ? ? ? ? ?
14, 46 ? ? ?? ???
2
x 14x 46 0 ? ? ? ?
11. 2
11. Q = 3R = 2(P + R)
Q = 2P + 2R
3R = 2P + 2R
R = 2P
? Q = 2P + 4P = 6P
? P + 6P + 2P = 180° ? 9P = 180° ? P = 20°
? Q = 6 × 20 = 120°
12. 2
12. ? ? ? ?
p x 3
,p x 3K,q x 3K
q x 3
?
? ? ? ? ?
?
? ? ? ?
? ? ? ?
2 2
2 2
2 2 2 2
x 3K x 3K
p q
p q
x 3K x 3K
? ? ? ? ? ? ?
?
? ? ? ?
?
?
? ? ? ? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ?
2 2
2 2
x 3 x 3
x 3 x 3
? ? ?
?
? ? ?
? ? ? ?
? ?
2
x3 x 3 x 3 x3
2 x 9
?? ? ???
?
?
? ?
2
2x 6
2 x 9
?
?
?
2
6x
x 9
?
?
13. 1
13. Perimeter of square = 4a = 2(l + b)
l = 24 = 2b ? b = 12
? 4a = 72 ? a = 18
? Area of square = 18
2
= 324
14. 1
14.
2
1 1
1 1 1
2
2 2 2
2 2
1
r h
V h h 2 1 8
3
1
V 3 4 h h 3
r h
3
?
? ? ? ? ? ?
?
15. 3
15. 2
x
= 8
y – 1
? x = 3y – 3 …(1)
9
y
= 3
x – 6
? 2y = x – 6 …(2)
by (1) & (2)
x = 24, y = 9
? x + y = 33
16. 1
16. x – y : (x + y) : xy = 1 : 7 : 24
x y 1
7x 7y x y
x y 7
?
? ? ? ? ?
?
= 6x = 8y
4
x y
3
? ?
2
4
y y
x y 1y 1 1
3
y 6
4
xy 4y 24 4y
y y
3
?
?
? ? ? ? ? ?
?
4
x 6 8
3
? ? ? ?
? xy = 48
17. 1
17. 6, 7, 7, 7, 9, 9, 14, 15
mode = 7
range = 15 – 6 = 9
median = 8
798
mean 8
3
? ?
? ? ?
18. 4
18. Let initial income be x
? initial expenditure = 0.8 x
New expenditure = 1.375 (0.8 x)
= 1.1 x
New income
7x
6
?
? Saving
7x 11x
6 10
? ?
2x x
30 15
? ?
x
5
15
present percent saving 100 5 %
7x
7
6
? ? ? ?
19. 3
19. Let the cost of 1 chair be ‘c’ and the cost of 1 table be ‘t’
5c + 3t = 3110
c = t – 210
So, we get,
5t – 1050 + 3t = 3110 ? 8t = 4160 ? t = 520
? c = 310
? Rs.1660
20. 2
20.
1
5 a
1
1
1
6
2
? ?
?
?
1
5 a
2
1
13
? ? ?
?
13
5 a
15
? ? ?
13
a 5
15
? ? ?
62
a
15
? ?
21. 4
21. Let number be x
7 5
x x 5
8 7
? ?
7x 5x
5
8 7
? ?
49x 40x 5 56
5 x
56 9
? ?
? ? ?
56
9x 9 5 5 56 280
9
? ? ? ? ? ? ?
22. 3
22. ? ?
2
3
1 4
6 24 R
3 3
? ? ? ? ? ?
? R = 6
? TSA = 4 ?R
2
= 4 × ? × 36 = 144 ? sq cm
23. 4
23.
1 1 1 1 1 1
2
P Q R 10 15 20
? ?
? ? ? ? ?
? ?
? ?
1 1 1 6 4 3 13
P Q R 60 2 60 2
? ?
? ? ? ?
? ?
11 1 11 13 1
PQ R PQ 120 10
? ?
? ? ? ? ? ?
? ?
? ?
1 13 12 1
R 120 120
?
? ? ?
R will complete in 120 days
24. 3
24.
1 1 1 1
3 3 2 2
3 ,2 ,2 ,4
3 3 2 2
666 6
3 ,2 ,2 ,4
? ? ? ? ? ? ? ?
1 1 1 1
3 2 3 2 6 6 6 6
3 ,2 ,2 , 4 ?
Page 5
NTSE STAGE – I (DELHI STATE)
05 – A (2018 – 19)
(For Class – X)
MENTAL ABILITY TEST (MAT)
HINTS & SOLUTIONS
1. 4
1. ? ?
2
2
25
x 10 x 10x 25 0 x 5 0 x 5
x
? ? ? ? ? ? ? ? ? ? ?
2
2
50 50
25 25 2 27
25
x
x
? ?? ?? ?
2. 1
2. x + y = 3, x
2
+ y
2
= 15
(x – y)
2
= ?, (x
2
+ y
2
+ 2xy) = 9 ? 15 + 2xy = 9
? xy = ?3
(x – y)
2
= x
2
+ y
2
– 2xy = 15 + 6 = 21
3. 2
3.
a b c
K a 3K,b 5K,c 7K
357
??? ? ? ? ?
a b c 3K 5K 7K
3
b 5K
? ? ? ?
? ? ?
4. 3
4. x + y = 25, x
2
+ y
2
= 425
? x
2
+ y
2
+ 2xy = 625
? 425 + 2xy = 625 ? xy = 100
5. 1
5.
2
0.64 a 64 ? ?
2
2
0.64 1 1
64 a a 0.1
100 10 a
? ? ? ? ? ? ?
6. 2
6. Dividend = divisor × quotient + remainder
Divisor = 30 × q
Divisor = 4 × r
? q = 20 ? Divisor ? 600 & remainder
600
150
4
? ?
Dividend 600 20 150 12,150 ? ? ? ? ?
7. 4
7. 3
a-2b
= 27 ?3
a – 2b
= 3
3
? a – 2b = 3 …(1)
9
a+b
= 3 ? 3
2a + 2b
= 3
1
? 2a + 2b = 1 …(2)
by equation (1) and (2)
5 4
3a 4 a ,b
3 6
? ? ? ? ?
?
4 / 3
a 8
b 5
5 / 6
? ?
? ? ? ?
? ?
?
? ?
8. 4
8. 17 x 11 11 6 2. 11. 6 ? ? ? ?
x 2 6 ? ?
2
x 24 ? ?
9. 1
9. 0.02 0.2 a 0.2 0.2 b ?? ? ??
0.02 0.2 a 0.2 0.2 0.2 0.2 b ? ? ? ? ????
a 0.2 0.2 0.2
0.4
b 0.02
? ?
? ? ?
10. 1
10. 7 3, 7 3 ? ? ? ? ? ?
14, 46 ? ? ?? ???
2
x 14x 46 0 ? ? ? ?
11. 2
11. Q = 3R = 2(P + R)
Q = 2P + 2R
3R = 2P + 2R
R = 2P
? Q = 2P + 4P = 6P
? P + 6P + 2P = 180° ? 9P = 180° ? P = 20°
? Q = 6 × 20 = 120°
12. 2
12. ? ? ? ?
p x 3
,p x 3K,q x 3K
q x 3
?
? ? ? ? ?
?
? ? ? ?
? ? ? ?
2 2
2 2
2 2 2 2
x 3K x 3K
p q
p q
x 3K x 3K
? ? ? ? ? ? ?
?
? ? ? ?
?
?
? ? ? ? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ?
2 2
2 2
x 3 x 3
x 3 x 3
? ? ?
?
? ? ?
? ? ? ?
? ?
2
x3 x 3 x 3 x3
2 x 9
?? ? ???
?
?
? ?
2
2x 6
2 x 9
?
?
?
2
6x
x 9
?
?
13. 1
13. Perimeter of square = 4a = 2(l + b)
l = 24 = 2b ? b = 12
? 4a = 72 ? a = 18
? Area of square = 18
2
= 324
14. 1
14.
2
1 1
1 1 1
2
2 2 2
2 2
1
r h
V h h 2 1 8
3
1
V 3 4 h h 3
r h
3
?
? ? ? ? ? ?
?
15. 3
15. 2
x
= 8
y – 1
? x = 3y – 3 …(1)
9
y
= 3
x – 6
? 2y = x – 6 …(2)
by (1) & (2)
x = 24, y = 9
? x + y = 33
16. 1
16. x – y : (x + y) : xy = 1 : 7 : 24
x y 1
7x 7y x y
x y 7
?
? ? ? ? ?
?
= 6x = 8y
4
x y
3
? ?
2
4
y y
x y 1y 1 1
3
y 6
4
xy 4y 24 4y
y y
3
?
?
? ? ? ? ? ?
?
4
x 6 8
3
? ? ? ?
? xy = 48
17. 1
17. 6, 7, 7, 7, 9, 9, 14, 15
mode = 7
range = 15 – 6 = 9
median = 8
798
mean 8
3
? ?
? ? ?
18. 4
18. Let initial income be x
? initial expenditure = 0.8 x
New expenditure = 1.375 (0.8 x)
= 1.1 x
New income
7x
6
?
? Saving
7x 11x
6 10
? ?
2x x
30 15
? ?
x
5
15
present percent saving 100 5 %
7x
7
6
? ? ? ?
19. 3
19. Let the cost of 1 chair be ‘c’ and the cost of 1 table be ‘t’
5c + 3t = 3110
c = t – 210
So, we get,
5t – 1050 + 3t = 3110 ? 8t = 4160 ? t = 520
? c = 310
? Rs.1660
20. 2
20.
1
5 a
1
1
1
6
2
? ?
?
?
1
5 a
2
1
13
? ? ?
?
13
5 a
15
? ? ?
13
a 5
15
? ? ?
62
a
15
? ?
21. 4
21. Let number be x
7 5
x x 5
8 7
? ?
7x 5x
5
8 7
? ?
49x 40x 5 56
5 x
56 9
? ?
? ? ?
56
9x 9 5 5 56 280
9
? ? ? ? ? ? ?
22. 3
22. ? ?
2
3
1 4
6 24 R
3 3
? ? ? ? ? ?
? R = 6
? TSA = 4 ?R
2
= 4 × ? × 36 = 144 ? sq cm
23. 4
23.
1 1 1 1 1 1
2
P Q R 10 15 20
? ?
? ? ? ? ?
? ?
? ?
1 1 1 6 4 3 13
P Q R 60 2 60 2
? ?
? ? ? ?
? ?
11 1 11 13 1
PQ R PQ 120 10
? ?
? ? ? ? ? ?
? ?
? ?
1 13 12 1
R 120 120
?
? ? ?
R will complete in 120 days
24. 3
24.
1 1 1 1
3 3 2 2
3 ,2 ,2 ,4
3 3 2 2
666 6
3 ,2 ,2 ,4
? ? ? ? ? ? ? ?
1 1 1 1
3 2 3 2 6 6 6 6
3 ,2 ,2 , 4 ?
? ? ? ? ? ? ? ?
1 1 1 1
6 6 6 6
27,4 ,8,16 ?
25. 4
25. Putting symbols in option (4)
8 × 8 + 8 ? 8 – 8 = 64 + 1 – 8 = 57
26. 4
26. Out of 60 litres 12 litres is taken out
12
i.e. 100 20%
60
? ?
milk remained after two replacement
80 80
60 38.4 litres
100 100
? ? ? ?
27. 4
27. Except option (4) all follows.
x : 3x + 1
28. 3
28. Between A and B ? 30 – 20 – 1 = 09
total = 20 + 9 + 16 = 45
29. 1
29.
15
n 5
3
? ?
one face painted = (n – 2)
2
× 6
= 3
2
× 6 = 54
30. 2
30. Let son’s present age ? s
S = 48 – 3S
? S = 12
Son is 12 years now, so 4 years ago he would be 8.
31. 2
31. Series follows
1 2, 3 4, 5 6, 7 8, 9 10, 11 12
56
? ???? ?
? ? ? ?
32. 4
32. 10 100 200 310 430
+90 +100 +110 +120
+10 +10 +10
33. 4
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