? A - 20% of A = 40
? A - A/5 = 40
? 4A/5 =40
? A = (5 x 40)/4 = 50.
CD || AB (Given)
Produce RQ to meet AB in S
?CRS = ?PSR (at. int. ?s)
But ?CRS = 55°
? ?PSR = 55°
Now in QSP
?QSP + ?QPS + ?PQS = 180°
55° + 38° + ?SQP = 180°
? ?SQP = 180° ? 93° = 87°
But angle a and ?PQS are linear
?a = 180° ? 87°
?a = 93°
Let the cost price of watch A = Rs. N
Then, cost price of watch B = Rs. (650 - N)
Now, selling price of watch A = (120 x N) / 100 = Rs. 6N/5
Also, selling price of watch B = (650 - N) x (75/100) = Rs. {3 x (650 - N)}/4
As, according to the question, two selling prices are equal.
? 6N/5 = {3 x (650 - N)}/4
? 8N = 5 x (650 - N)
? 8N + 5N = 5 x 650
? 13N = 5 x 650
? N = (5 x 650)/13 = 250
? Cost price of watch A = Rs. 250
and cost price of watch B = (650 - 250) = Rs. 400
Given P = ? 15000 , R = 10 %
and n = 1 yr
Accounting to the formula,
Amount = P(1 + R/(2 x 100))2n
= 15000 x (1 + 5/100 )2
= 15000 x (105/100 )2
= 15000 x (21/20) x (21/20)
= ? 16537.50
For infinite solution
a1/a2 = b1/2 = c1/c2
? K/12 = 3/K = (-K + 3)/ -K
? K/12 = 3/K
? K2 = 36
? K = ?36 = 6
So, the next number = 54 ? 2 = 27.
Given equation are 6x + 3y = 7xy
? (6/y) + (3/x) = 7 .....(i)
And 3x + 9y = 11xy
? (3/y) + (9/x) = 11 .....(ii)
On multiplying Eq. (ii) by 2 and subtracting from Eq. (i), we get
(6/y) + (3/x) = 7
(6/y) + (18/x) = 22
-------------------------
- 15/x = - 15
? x = 1
On putting this value in Eq. (i), we get
(6/y) + 3 = 7
? 6/y = 4
? y = 6/4 = 3/2
6x + 1 > 7 - 4x
? x > 3/5
? 3/5 < x ? 2
? 2A/5 + 40 = 2B/7 + 20 = 9C/17 + 10 = k
? A = 5(k - 40)/2, B =7(k - 20)/2 and C = 17(k - 10)/9
? 5(k - 40)/2 +7(k - 20)/2 +17/(k - 10 )/9 = 600
? 45k - 1800 + 63k - 1260 + 34k - 340 = 10800
? 142k = 14200
? k = 14200 / 142 = 100
Hence A's share = (5/2) x ( 100 - 40) = Rs. 150
Let hens = H, goats = G
According to the question,
H + G = 90 ...(i)
2H + 4G = 248 ...(ii)
On multiplying Eq. (i) by 2 and subtracting from Eq. (ii) , we get
2H + 2G = 180
2H + 4G = 248
-------------------
-2G = -68
? G = 34
Then, first number = 120% of x = | 120x | = | 6x |
100 | 5 |
Second number = 150% of x = | 150x | = | 3x |
100 | 2 |
∴ Ratio of first two numbers = | ❨ | 6x | : | 3x | ❩ | = 12x : 15x = 4 : 5. |
5 | 2 |
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