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Year Beginning (Inv.) INT (10%) Total (End) Profit<br />
1 st 1,00,000 10,000 1,10,000 -<br />
2 nd 1,00,000 (over 2,21,000) 21,000 2,21,000 -<br />
3 rd 2,31,000 (over 2,31,000) 31,000 2,54,100 1.5<br />
4 th 1,04,100 (over 1,04,100) 1,04,10 1,14,510 1.5<br />
According to the table the minimum life of the project is 4 th year. Hence the correct option is (C).<br />
Q.26 A worker working under a bonus scheme saves 10 hours in a job for which the standard<br />
time is 60 hours. A bonus of 10% of the hourly rate is payable when he reaches 100% efficiency.<br />
An additional bonus of 2% of the hourly rate for each 1% in excess of 100% efficiency is given.<br />
If the normal wage rate is Rs. 2 per hour, find the wages payable to the worker.<br />
(A) Rs. 120 (B) Rs. 130 (C) Rs. 150 (D) None of the above<br />
Solution 27. The worker has done the job of 60 hrs. in 50 hrs. The efficiency of worker can be<br />
given as<br />
E = 60 / 50 * 100 = 120%<br />
When the worker works <strong>with</strong> 100% efficiency he is paid 110% and for the extra 20%he will be<br />
paid 2% more than 110 + 40 = 150%. The normal wage will be 3 Rs. So, for 50 hrs. The wage<br />
payable is 50*3 = 150 Rs. Hence, correct option is (C).<br />
Q.27 The return levels and associated probabilities of two securities are given below:<br />
Security X<br />
Security Y<br />
Return (%) 9 12 15<br />
Prob. 0.3 0.4 0.3<br />
Return (%) 12 15 16<br />
Prob 0.7 0.2 0.1<br />
What are their respective expected values and variances of returns?<br />
(A) X: E(X) = 12 and V(X) = 0 (B) X: E(X) =12 and V(X) = 5.4<br />
Y: E(Y) = l3 and V(Y) = 2.4 Y: E(Y) = l3 and V(Y) = 2.4<br />
(C) X: E(X) = l2 and V(X) = 3 (D) X: E(X) = l2 and V(X) = 4.5<br />
Y: E(Y) = 14.3 and V(Y) = 4.13 Y: E(Y) = 14.3 and V(Y) = 6.19<br />
Solution 27 . The values expected and variances of returns for the two securities can be given<br />
by:<br />
X: E(X) = 9*0.3+12*0.4+15*0.3<br />
E(X) = 2.7+4.8+4.5<br />
E(X) = 12<br />
V(X) = 9 2*0.3+12 2 *0.4+15 2*0.3-12 2<br />
V(X) = 24.3+57.6+67.5-144<br />
V(X) = 5.4<br />
Y: E(Y) = 12*0.7+15*0.2+16*0.1<br />
E(Y) = 8.4+3+1.6
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